problem solving volume of cylinder

Volume of Cylinders

A cylinder is a solid with two congruent circles joined by a curved surface.

In the above figure, the radius of the circular base is r and the height is h.

The volume of the cylinder is the area of the base × height. Since the base is a circle and the area of a circle is πr 2 then the volume of the cylinder is πr 2 × h.

Volume of cylinder = πr 2 h

Surface Area of cylinder = 2πr 2 + 2πrh

Calculate the volume of a cylinder where:

a) the area of the base is 30 cm 2 and the height is 6 cm. b) the radius of the base is 14 cm and the height is 10 cm.

Sometimes you may be required to calculate the volume of a hollow cylinder or tube or pipe.

Volume of hollow cylinder: = πR 2 h – πr 2 h = πh (R 2 – r 2 )

The figure shows a section of a metal pipe. Given the internal radius of the pipe is 2 cm, the external radius is 2.4 cm and the length of the pipe is 10 cm. Find the volume of the metal used.

Solution: The cross section of the pipe is a ring: Area of ring = [ π (2.4) 2 – π (2) 2 ]= 1.76 π cm 2

These videos show how to solve word problems about cylinders.

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Volume of a cylinder

Here you will learn about the volume of a cylinder, including how to calculate the volume of a cylinder given its radius, area and perpendicular height.

Students will first learn about volume of cylinders as part of geometry in grade 7 and again in grade 8 and high school geometry.

What is the volume of a cylinder?

The volume of a cylinder is the amount of space there is inside a cylinder.

In order to find the volume of a cylinder you first need to find the circular area of the base.

To do this, you can use the formula for calculating the area of a circle, which is

Then multiply the area of the circular base by the height (or length) of the cylinder.

To do this, you can use the formula for the volume of a cylinder , which is

Where \textbf{r} is the radius of a cylinder and \textbf{h} is the perpendicular height of a cylinder.

For example, find the volume of this cylinder with radius of the base 7~cm and perpendicular height 10~cm.

Common Core State Standards

How does this relate to 7 th grade and high school math?

• Grade 7 – Geometry (7.G.B.6) Solve real-world and mathematical problems involving area, volume and total surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
• High School – Geometry (HSG.GMD.A.3) Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

[FREE] Volume Check for Understanding Quiz (Grade 6 to 8)

Use this quiz to check your grade 6 to 8 students’ understanding of volume. 10+ questions with answers covering a range of 6th, 7th and 8th grade volume topics to identify areas of strength and support!

How to calculate the volume of a cylinder

• Write down the formula: \text{Volume} = \pi r^2 h

Substitute the given values.

Work out the calculation.

Write the final answer, including units.

Volume of a cylinder examples

Example 1: volume of a cylinder.

Find the volume of the cylinder with radius 3~cm and perpendicular height 5~cm.

Give your answer to 1 decimal place.

Write down the formula.

To answer the question you need the formula for the volume of a cylinder.

2 Substitute the given values.

Substitute the value of the radius r and the perpendicular height h into the formula.

3 Work out the calculation.

Use a calculator to work out the volume.

4 Write the final answer, including units.

Check what form the final answer needs to be written in. You may need to leave your answer in terms of \pi or as a decimal with rounding. Here you are asked to give the answer to 1 decimal place.

The volume of the cylinder is: 141.4 \mathrm{~cm}^3.

Example 2: volume of a cylinder

Find the volume of the cylinder with radius 4.8~cm and perpendicular height 7.9~cm.

Give your answer to 3 significant figures.

\text { Volume }=\pi r^2 h

V=\pi \times 4.8^2 \times 7.9

Check what form the final answer needs to be.

You may need to leave your answer in terms of \pi or as a decimal with rounding.

Here you are asked to give the answer to 3 significant figures.

V=571.820=572 \mathrm{~cm}^3

The volume of the cylinder is: 572 \mathrm{~cm}^3.

Example 3: volume of a cylinder

Find the volume of the cylinder with radius 3~cm and perpendicular height 7~cm.

Leave your answer in terms of \pi.

Write down the formula .

V=\pi \times 3^2 \times 7

Work out the volume. (Focusing on the number parts of the calculation).

Check what form the final answer needs to be written in. You may need to leave your answer in terms of \pi or as a decimal with rounding.

V=63 \pi=63 \pi \mathrm{~cm}^3

The volume of the cylinder is: 63 \pi \mathrm{~cm}^3.

Example 4: volume of a cylinder

Find the volume of the cylinder with radius 4~cm and perpendicular height 10~cm.

V=\pi \times 4^2 \times 10

V=160 \pi=160 \pi \mathrm{~cm}^3

The volume of the cylinder is: 160 \pi \mathrm{~cm}^3.

Example 5: using the formula to find a length

The volume of a cylinder is 1600~cm^3. Its radius is 9~cm. Find its perpendicular height. Give your answer to 2 decimal places.

The question involves the volume of a cylinder, so you need the formula for the volume of a cylinder.

V=\pi r^2 h

You are given the volume and the radius, so substitute these into the formula.

1600=\pi \times 9^2 \times h

You need to rearrange the formula to find the value of h.

1600=\pi \times 81 \times h

\cfrac{1600}{\pi \times 81}=h

Here you are asked to give the answer to 2 decimal places.

h=6.287=6.29 \mathrm{~cm}

The perpendicular height of the cylinder is: 6.29~cm.

Example 6: using the formula to find a length

The volume of a cylinder is 1400~cm^3. Its perpendicular height is 15~cm. Find its radius. Give your answer to 2 decimal places.

You are given the volume and the perpendicular height, so substitute these into the formula.

1400=\pi \times r^2 \times 15

\cfrac{1400}{\pi \times 15}=r^2

r^2=29.70892

r=\sqrt{29.70892}

Check what form the final answer needs to be written in.

r=\sqrt{29.70892}=5.4505=5.45 \mathrm{~cm}

The radius of the cylinder is: 5.45~cm.

Teaching tips for volume of a cylinder

• Implement engaging visual aids and real-world examples to illustrate how the formula applies, fostering a deeper comprehension of 3d shapes. Using visual aids will also help English Language Learners comprehend the complexity of the three dimensional space and three-dimensional shapes.
• Incorporate interactive activities and group exercises that encourage hands-on exploration of cylinder volume calculations, ensuring students actively participate in the learning process. Incorporating open-ended tasks for students to find the surface area of a cylinder, cuboid, or oblique cylinder as well as a focus on the area of the cylinder and base of the cylinder will scaffold student learning appropriately.
• Provide step-by-step problem-solving tutorials, addressing common challenges students might encounter when finding the volume of a cylinder, thereby enhancing the accessibility and usefulness of your educational content.
• Highlight the importance of exposing students to diverse cubic units such as cubic inches, cubic centimeters, cubic meters, and cubic feet, as it not only reinforces the concept of volume but also fosters a versatile and practical comprehension of three-dimensional space.

Easy mistakes to make

• Incorrect radius calculation When finding the volume of a cylinder, be cautious not to miscalculate the radius, as errors in this fundamental measurement can lead to inaccuracies in the final volume. Emphasize the importance of doubling the radius squared and verify calculations to prevent mistakes.
• Misinterpreting height measurements Avoid the mistake of misinterpreting or inaccurately measuring the height of the cylinder. Stress the need for precision in obtaining height values, and remind students to double-check measurements to ensure accuracy in volume calculations.
• Omitting units in the final answer In the excitement of solving volume problems, it’s easy to overlook including the appropriate units in the final answer. Remind students to always attach the correct cubic units (cubic inches, cubic centimeters, cubic feet, cubic meters, etc.) to their volume results, enhancing clarity and correctness.
• Neglecting the order of operations Students may inadvertently neglect the proper order of operations when applying the volume formula. Reinforce the importance of parentheses and guiding students to follow the correct sequence to prevent errors in their calculations.
• Overlooking the \textbf{P}\,\textbf{i} value Students may forget to incorporate the value of Pi accurately, leading to significant errors in volume calculations. Stress the consistent use of the correct \pi value and caution against rounding too early in the calculation process to maintain precision in results.

Related volume lessons

• Volume of a rectangular prism
• Volume of a hemisphere
• Volume of a prism
• Volume of a sphere
• Volume of a cone
• Volume of a cube
• Volume of a triangular prism
• Volume of a pyramid
• Volume of square pyramid
• Volume formula

Practice volume of a cylinder questions

1) Find the volume of a cylinder with a radius 3.2~cm and perpendicular height 9.1~cm. Give your answer to 3 significant figures.

You are finding the volume of a cylinder so substitute the value of r and h into the formula.

2) Find the volume of a cylinder with a radius 5.3~cm and perpendicular height 3.8~cm. Give your answer to 3 significant figures.

3) Find the volume of a cylinder with a radius 8~cm and perpendicular height 7~cm. Leave your answer in terms of \pi.

4) Find the volume of a cylinder with a radius 4~cm and perpendicular height 8~cm. Give your answer to 3 significant figures.

5) The volume of a cylinder is 250~cm^3. Its radius is 2.9~cm. Find its perpendicular height. Give your answer to 2 decimal places.

Using the formula, substitute the value of the volume and the value of the radius and rearrange to find the radius.

6) The volume of a cylinder is 800~cm^3. Its perpendicular height is 9.2~cm. Find its radius. Give your answer to 2 decimal places.

Using the formula, substitute the value of the volume and the value of the perpendicular height and rearrange to find the radius.

Volume of a cylinder FAQs

Common mistakes include misinterpreting height measurements, miscalculating the radius, and omitting units. Learn to recognize and avoid these errors for accurate volume calculations. Additionally, double-check your calculations and ensure you follow the correct order of operations.

Yes, you can use various cubic units, such as cubic inches or cubic centimeters, when calculating cylinder volume. Understanding different units provides versatility in solving real-world problems. Be consistent with your unit usage to maintain precision in your answers.

Ensure accuracy by consistently using the appropriate Pi value throughout your calculations. Maintain precision by avoiding premature rounding in the process. Remember to keep \pi in your calculations until the final step for accurate results.

Engage in hands-on activities like measuring the volume of cylindrical objects such as cans or jars. These real-world examples enhance your grasp of the volume formula and its applications. Experiment with various objects to reinforce the concept and its practical implications in different scenarios.

The next lessons are

• Surface area
• Pythagorean theorem
• Trigonometry

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Volume of Cylinder

The volume of a cylinder is the capacity of the cylinder which calculates the amount of material quantity it can hold. In geometry, there is a specific formula to calculate the volume of a cylinder that is used to measure how much amount of any quantity whether liquid or solid can be immersed in it uniformly. A cylinder is a three-dimensional shape with two congruent and parallel identical bases. There are different types of cylinders. They are:

• Right circular cylinder: A cylinder whose bases are circles and each line segment that is a part of the lateral curved surface is perpendicular to the bases.
• Oblique Cylinder: A cylinder whose sides lean over the base at an angle that is not equal to a right angle.
• Elliptic Cylinder: A cylinder whose bases are ellipses.
• Right circular hollow cylinder: A cylinder that consists of two right circular cylinders bounded one inside the other.

The formula to find the volume of a cylinder is V = πr 2 h. Let us learn more about this formula in the upcoming sections.

What is the Volume of a Cylinder?

The volume of a cylinder is the number of unit cubes (cubes of unit length) that can be fit into it. It is the space occupied by the cylinder as the volume of any three-dimensional shape is the space occupied by it. The volume of a cylinder is measured in cubic units such as cm 3 , m 3 , in 3 , etc. Let us see the formula used to calculate the volume of a cylinder.

Definition of a Cylinder

A cylinder is a three-dimensional solid shape that consists of two parallel bases linked by a curved surface. These bases are like a circular disk in a shape . The line passing from the center or joining the centers of two circular bases is called the axis of the cylinder.

Volume of Cylinder Formula

We know that a cylinder resembles a prism (but note that a cylinder is not a prism as it has a curved side face), we use the same formula of volume of a prism to calculate the volume of a cylinder as well. We know that the volume of a prism is calculated using the formula,

V = A × h, where

• A = area of the base

Using this formula, the formulas of volume of cylinder are:

• The formula for volume of a right circular cylinder is, V = πr 2 h (r = radius, h = height)
• The formula for volume of an oblique cylinder is, V = πr 2 h (r = radius, h = height)
• The formula for volume of an elliptic cylinder is, V = πabh (a and b = radii, h = height)
• The formula for volume of a right circular hollow cylinder is, V = π(R 2 - r 2 )h (R = outer radius, r = inner radius, h = height)

Now we will apply the formula V = A × h to calculate the volume of different types of cylinders.

Volume of a Right Circular Cylinder Formula

We know that the base of a right circular cylinder is a circle and the area of a circle of radius 'r' is πr 2 . Thus, the volume (V) of a right circular cylinder, using the above formula (V = A × h), is,

• 'r' is the radius of the base (circle) of the cylinder
• 'h' is the height of the cylinder
• π is a constant whose value is either 22/7 (or) 3.142.

Thus, the volume of cylinder directly varies with its height and directly varies with the square of its radius. i.e., if the radius of the cylinder becomes double, then its volume becomes four times.

Formula to Find Volume of an Oblique Cylinder

The formula to calculate the volume of cylinder (oblique) is the same as that of a right circular cylinder. Thus, the volume (V) of an oblique cylinder whose base radius is 'r' and whose height is 'h' is,

Formula to Calculate Volume of an Elliptic Cylinder

We know that an ellipse has two radii. Also, we know that the area of an ellipse whose radii are 'a' and 'b' is πab. Thus, the volume of an elliptic cylinder is,

• 'a' and 'b' are the radii of the base (ellipse) of the cylinder.
• 'h' is the height of the cylinder.

Volume of a Right Circular Hollow Cylinder Formula

As a right circular hollow cylinder is a cylinder that consists of two right circular cylinders bounded one inside the other, its volume is obtained by subtracting the volume of the inside cylinder from that of the outside cylinder. Thus, the volume (V) of a right circular hollow cylinder is,

V = π(R 2 - r 2 )h

• 'R' is the base radius of the outside cylinder.
• 'r' is the base radius of the inside cylinder.
• π is a constant whose value is 22/7 (or) 3.142.

How To Find the Volume of Cylinder?

Here are the steps to find the volume of cylinder:

• Identify the radius to be 'r' and height to be 'h' and make sure that they both are of the same units.
• Substitute the values in the volume formula V = πr 2 h.
• Write the units as cubic units.

Example: Find the volume of a right circular cylinder of radius 50 cm and height 1 meter. Use π = 3.142.

The radius of the cylinder is, r = 50 cm.

Its height is, h = 1 meter = 100 cm.

Its volume is, V = πr 2 h = (3.142)(50) 2 (100) = 785,500 cm 3 .

Note: We need to use the formula to find the volume of a cylinder depending on its type as we discussed in the previous section. Also, assume that a cylinder is a right circular cylinder if there is no type given and apply the volume of a cylinder formula to be V = πr 2 h.

Important Notes on Volume of Cylinder:

• The volume of a cylinder is calculated using the formula, V = πr 2 h, where r is the radius of its circular base and 'h' is the perpendicular distance (height) between the centres of the bases.
• If diameter (d) is given, then find the radius (r) using r = d/2 and then substitute in the above formula to find the volume of cylinder.

Volume of Cylinder Examples

Example 1: Find the volume of a cylindrical water tank in litres whose base radius is 25 m and whose height is 120 m. Use π = 3.14.

The radius of the cylindrical tank is, r = 25 m.

Its height is, h = 120 m.

Using the formula of volume of cylinder, the volume of the tank is,

V = (3.14)(25) 2 (120) = 235500 cubic meters.

The volume of a cylinder in litres is obtained by using the conversion formula 1 cubic meter = 1000 liters.

Thus, the volume of the tank in liters is: 235500 × 1000 = 235,500,000

Answer: The volume of the given cylindrical tank is 235,500,000 liters.

Example 2: Calculate the volume of an elliptic cylinder whose base radii are 7 inches and 10 inches, and whose height is 15 inches. Use π = 22/7.

The base radii of the given elliptic cylinder are,

a = 7 inches and b = 10 inches.

Its height is, h = 15 inches.

Using the volume of cylinder formula, the volume of the given elliptic cylinder is,

V = (22/7) × 7 × 10 × 15 = 3300 cubic inches.

Answer: The volume of the given cylinder is 3,300 cubic inches.

Example 3: What is the volume of the cylinder with a radius of 4 units and a height of 6 units?

Since the exact type of cylinder is not mentioned, we need to assume it is a right circular cylinder.

Radius,r = 4 units and height,h = 6 units

Volume of the cylinder, V = πr 2 h cubic units.

V = (22/7) × (4) 2 × 6 V = 22/7 × 16 × 6

V= 301.71 cubic units.

Answer: The volume of the cylinder is 301.71 cubic units.

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Practice Questions on Volume of Cylinder

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FAQs on Volume of Cylinder

What is the meaning of volume of cylinder.

The volume of a cylinder is the amount of space in it. It can be obtained by multiplying its base area by its height. The formula to find the  volume of a cylinder of base radius 'r' and height 'h' is V = πr 2 h.

What Is the Formula for Calculating the Volume of a Cylinder?

The formula for calculating the volume of a cylinder is V = πr 2 h, where

• 'r' is the radius of the base of the cylinder
• π is a constant whose value is equal to approximately 3.142.

What is the Volume of a Cylinder with Diameter?

Let us consider a cylinder of radius 'r', diameter 'd', and height 'h'. The volume of a cylinder of base radius 'r' and height 'h' is V = πr 2 h. We know that r = d/2. By substituting this in the above formula, V = πd 2 h/4.

What Is the Ratio of the Volume of a Cylinder and a Cone?

Let us consider a cylinder and a cone , each with base radius 'r' and height 'h'. We know that the volume of the cylinder is πr 2 h and the volume of the cone is 1/3 πr 2 h. Thus the required ratio is 1:(1/3) (or) 3:1.

How To Calculate Volume of a Cylinder With Diameter and Height?

The volume of a cylinder with base radius 'r' and height 'h' is, V = πr 2 h. If its base diameter is d, then we have d = r/2. Substituting this in the above formula, we get V = πd 2 h/4. Thus, the formula to find the volume of a cylinder with the diameter (d) and height(h) is V = πd 2 h/4.

How To Find Volume of Cylinder With Circumference and Height?

We know that the circumference of a circle of radius 'r' is C = 2πr. Thus, when the circumference of the base of a cylinder (C) and its height (h) are given, then we first solve the equation C = 2πr for 'r' and then we apply the volume of a cylinder formula, which is, V = πr 2 h.

How To Calculate Volume of Cylinder in Litres?

We can use the following conversion formulas to convert the volume of cylinder from m 3 (or) cm 3 to liters.

• 1 m 3 = 1000 liters
• 1 cm 3 = 1 ml (or) 0.001 liters
• Metric Conversion
• Unit Conversion

What Happens to the Volume of Cylinder When Its Radius Is Halved?

The volume of cylinder varies directly with the square of its radius. Thus, when its radius is halved, the volume becomes 1/4 th .

What Happens to the Volume of Cylinder When Its Radius Is Doubled?

We know that the volume of cylinder is directly proportional to the square of its radius. Thus, when its radius is doubled, the volume becomes four times.

How Do You Find Volume of Cylinder Using Calculator?

Volume of a cylinder calculator is a machine to calculate a cylinder's volume. To calculate the volume of a cylinder using a calculator we need to provide necessary inputs to the calculator tool, such as required dimensions like radius, diameter, height, etc. Try now the volume of a cylinder calculator enter the radius and height of the cylinder in the given box of the volume of a cylinder calculator. Click on the "Calculate" button to find the volume of a cylinder. By clicking the "Reset" button you can easily clear the previously entered data and find the volume of a cylinder for different values.

☛Also Check:

• Cylinder Calculator
• Surface Area of Cylinder Calculator
• Height of a Cylinder Calculator

What is the Area and Volume of a Cylinder?

The surface area of a cylinder is the total area or region covered by the surface of the cylinder. The surface area of a cylinder is given by two following formulas:

• The curved surface area of cylinder = 2πrh
• The total surface area of the cylinder = 2πr 2 +2πrh = 2πr(h+r)

The area of a cylinder is expressed in square units, like m 2 , in 2 , cm 2 , yd 2 , etc.

The volume of a cylinder is the total amount of capacity immersed in a cylinder that can be calculated using the volume of cylinder equation is V = πr 2 h and it is measured in cubic units.

• Surface Area of Cylinder Worksheets
• Volume of a Cylinder Worksheets
• Surface Area Formulas

How Does the Volume of a Hollow Cylinder Change When the Height is Doubled?

The volume of a hollow cylinder formula is V = π(R 2 - r 2 )h cubic units. According to the volume formula, we can see that volume is directly proportional to the height of the hollow cylinder. Therefore, the volume gets doubled when the height of the hollow cylinder is doubled.

What is the Volume of Cylinder in Terms of Pi?

The volume of cylinder is defined as the capacity of a cylinder which is indicated in terms of pi. The volume of a cylinder in terms of pi is expressed in cubic units where units can be m 3 , cm 3 , in 3 , ft 3 , etc.

Cylinder Volume Calculator

How to calculate volume of a cylinder, volume of a hollow cylinder, volume of an oblique cylinder.

Our cylinder volume calculator enables calculating the volume of that solid. Whether you want to figure out how much water fits in a can, coffee in your favorite mug, or even the volume of a drinking straw – you're in the right place. The other option is calculating the volume of a cylindrical shell (hollow cylinder).

Let's start from the beginning – what is a cylinder? It's a solid bounded by a cylindrical surface and two parallel planes. We can imagine it as a solid physical tin having lids on top and bottom. To calculate its volume, we need to know two parameters – the radius (or diameter) and height:

cylinder volume = π × cylinder radius² × cylinder height

The cylinder volume calculator helps in finding the volume of right, hollow and oblique cylinders:

The hollow cylinder, also called the cylindrical shell, is a three-dimensional region bounded by two right circular cylinders having the same axis and two parallel annular bases perpendicular to the cylinders' common axis.

It's easier to understand that definition by imagining, e.g., a drinking straw or a pipe – the hollow cylinder is this plastic, metal, or other material. The formula behind the volume of a hollow cylinder is:

cylinder_volume = π × (R² - r²) × cylinder_height

where R – external radius, and r – internal radius

Similarly, we can calculate the cylinder volume using the external diameter, D , and internal diameter, d , of a hollow cylinder with this formula:

cylinder_volume = π × [(D² - d²)/4] × cylinder_height

To calculate the volume of a cylindrical shell, let's take some real-life examples, maybe... a roll of toilet paper, because why not? 😀

Enter the external diameter of the cylinder . The standard is equal to approximately 11 cm.

Determine the internal cylinder diameter . It's the internal diameter of the cardboard part, around 4 cm.

Find out what's the height of the cylinder ; for us, it's 9 cm.

Tadaaam! The volume of a hollow cylinder is equal to 742.2 cm³.

Remember that the result is the volume of the paper and the cardboard. If you want to calculate how much plasticine you can put inside the cardboard roll, use the standard formula for the volume of a cylinder – the calculator will calculate it in the blink of an eye!

The oblique cylinder is the one that 'leans over' – the sides are not perpendicular to the bases in contrast to a standard 'right cylinder'. How to calculate the volume of an oblique cylinder? The formula is the same as for the straight one. Just remember that the height must be perpendicular to the bases.

Now that you know how to calculate a volume of a cylinder, maybe you want to determine the volumes of other 3D solids? Use this general volume calculator !

If you are curious about how many teaspoons or cups fit into your container, use our volume converter .

To calculate the volume of soil needed for flower pots of different shapes – also for the cylindrical one – use the potting soil calculator .

Where can you find cylinders in nature?

Cylinders are all around us , and we are not just talking about Pringles’ cans. Although things in nature are rarely perfect cylinders, some examples are tree trunks & plant stems, some bones (and therefore bodies), and the flagella of microscopic organisms. These make up a large amount of the natural objects on Earth!

How do you draw a cylinder?

To draw a cylinder, follow these steps:

Draw a slightly flattened circle. The more flattened it is, the closer you are to looking at the cylinder side on .

Draw two equal, parallel lines from the far sides of your circle going down.

Link the ends of the two lines with a semi-circular line that looks the same as the bottom half of your top circle.

Add shadow and shading as appropriate.

How do you calculate the weight of a cylinder?

To calculate the weight of a cylinder:

Square the radius of the cylinder .

Multiply the square of radius by pi and the cylinder’s height .

Multiply the volume by the density of the cylinder. The result is the cylinder’s weight.

How do you calculate the surface area to volume ratio of a cylinder?

Find the volume of the cylinder using the formula πr²h .

Find the surface area of the cylinder using the formula 2πrh + 2πr² .

Make a ratio out of the two formulas, i.e., πr²h : 2πrh + 2πr² .

Alternatively, simplify it to rh : 2(h+r) .

Divide both sides by one of the sides to get the ratio in its simplest form.

How do you find the height of a cylinder?

If you have the volume and radius of the cylinder:

• Make sure the volume and radius are in the same units (e.g., cm³ and cm).

Square the radius.

• Divide the volume by the radius squared and pi to get the height in the same units as the radius.

If you have the surface area and radius (r):

• Make sure the surface and radius are in the same units .
• Subtract 2πr² from the surface area.
• Divide the result of step 2 by 2πr.
• The result is the height of the cylinder.

How do I find the radius of a cylinder?

If you have the volume and height of the cylinder:

• Make sure the volume and height are in the same units (e.g., cm³ and cm).
• Divide the volume by pi and the height.
• Square root the result.

If you have the surface area and height (h):

• Substitute the height, h, and surface area into the equation, surface area = 2πrh + 2πr².
• Divide both sides by 2π.
• Subtract surface area/2π from both sides.
• Solve the resulting quadratic equation.
• The positive root is the radius.

How do you find the volume of an oval cylinder?

To find the volume of an oval cylinder:

Multiply the smallest radius of the oval (minor axis) by its largest radius (major axis).

Multiply this new number by pi .

Divide the result of step 2 by 4. The result is the area of the oval.

Multiply the area of the oval by the height of the cylinder.

The result is the volume of an oval cylinder.

How do you find the volume of a slanted cylinder?

To calculator the volume of a slanted cylinder:

Find the radius, side length, and slant angle of the cylinder.

Multiply the result by pi.

Take the sin of the angle .

Multiply the sin by the side length.

Multiply the result from steps 3 and 5 together.

The result is the slanted volume.

How do you calculate the swept volume of a cylinder?

To compute the swept volume of a cylinder:

Divide the bore diameter by 2 to get the bore radius .

Square the bore radius.

Multiply the square radius by pi.

Multiply the result of step 3 by the length of the stroke . Make sure the units for bore and stroke length are the same.

The result is the swept volume of one cylinder.

Circumference

Heptagon area, steps to calories, triangular pyramid volume.

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Volume of a Cylinder Worksheets

This compilation of printable volume of a cylinder worksheets comes handy in providing 8th grade and high school students with sound knowledge in determining the volume of cylinders. Bolster practice with exercises presented as 3D shapes and as word problems involving real-life scenarios with dimensions expressed as integers and decimals. Find the radius from the diameter, figure out the volume, learn to convert to specified units and solve for missing dimensions too. Kick into gear with our free worksheets!

Volume of a Cylinder | Integers - Easy

Explain the volume of a cylinder formula and assist students in applying it to solve mathematical and real-life word problems. The height and radius of the cylinders are expressed as integers.

• Download the set

Volume of a Cylinder | Integers - Moderate

The height and diameter (or radius) of each cylindrical object are provided. Divide the diameter by 2 to determine the radius. Use the formula V = πr 2 h to compute the volume.

Volume of a Cylinder | Integers - Difficult

Intensify practice with this batch of pdf volume of a cylinder worksheets for grade 8. The dimensions are expressed in different units of measurement. Convert the units to the one specified and then find the volume.

Volume of a Cylinder | Decimals - Easy

Each dimension of the cylinder is presented as a decimal measure. Figure out the volume of each cylinder by plugging in the dimensions in the volume formula. Solve real-life word problems too.

Volume of a Cylinder | Decimals - Moderate

Determine the radius from the diameter. Apply the volume of a cylinder formula V = πr 2 h, substitute the value of the radius and height in the formula and compute the volume of each cylinder.

Volume of a Cylinder | Decimals - Difficult

Augment your practice in finding the volume of cylinders involving unit conversions. Direct students to convert the units in the dimensions to the indicated unit and then determine the volume.

Missing Parameter | Level 1

Walk through this batch of high school pdf worksheets with volume presented in terms of pi. Rearrange the formula, making the missing parameter the subject, substitute the known values and solve for the missing dimension.

Missing Parameter | Level 2

Assign the values of the volume and the radius or height and also the value of pi in the rearranged volume formula. Compute and find the missing height or radius in these printable volume of a cylinder worksheets.

Related Worksheets

» Volume of Cubes

» Volume of Cones

» Volume of Spheres and Hemispheres

» Volume of Prisms

» Volume of Composite Shapes

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Volume Problem Solving

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To solve problems on this page, you should be familiar with the following: Volume - Cuboid Volume - Sphere Volume - Cylinder Volume - Pyramid

This wiki includes several problems motivated to enhance problem-solving skills. Before getting started, recall the following formulas:

• Volume of sphere with radius \(r:\) \( \frac43 \pi r^3 \)
• Volume of cube with side length \(L:\) \( L^3 \)
• Volume of cone with radius \(r\) and height \(h:\) \( \frac13\pi r^2h \)
• Volume of cylinder with radius \(r\) and height \(h:\) \( \pi r^2h\)
• Volume of a cuboid with length \(l\), breadth \(b\), and height \(h:\) \(lbh\)

Volume Problem Solving - Basic

Volume - problem solving - intermediate, volume problem solving - advanced.

This section revolves around the basic understanding of volume and using the formulas for finding the volume. A couple of examples are followed by several problems to try.

Find the volume of a cube of side length \(10\text{ cm}\). \[\begin{align} (\text {Volume of a cube}) & = {(\text {Side length}})^{3}\\ & = {10}^{3}\\ & = 1000 ~\big(\text{cm}^{3}\big).\ _\square \end{align}\]

Find the volume of a cuboid of length \(10\text{ cm}\), breadth \(8\text{ cm}\). and height \(6\text{ cm}\). \[\begin{align} (\text {Area of a cuboid}) & = l × b × h\\ & = 10 × 8 × 6\\ & = 480 ~\big(\text{cm}^{3}\big).\ _\square \end{align}\]

I made a large ice cream cone of a composite shape of a cone and a hemisphere. If the height of the cone is 10 and the diameter of both the cone and the hemisphere is 6, what is the volume of this ice cream cone? The volume of the composite figure is the sum of the volume of the cone and the volume of the hemisphere. Recall the formulas for the following two volumes: \( V_{\text{cone}} = \frac13 \pi r^2 h\) and \( V_{\text{sphere}} =\frac43 \pi r^3 \). Since the volume of a hemisphere is half the volume of a a sphere of the same radius, the total volume for this problem is \[\frac13 \pi r^2 h + \frac12 \cdot \frac43 \pi r^3. \] With height \(h =10\), and diameter \(d = 6\) or radius \(r = \frac d2 = 3 \), the total volume is \(48\pi. \ _\square \)

Find the volume of a cone having slant height \(17\text{ cm}\) and radius of the base \(15\text{ cm}\). Let \(h\) denote the height of the cone, then \[\begin{align} (\text{slant height}) &=\sqrt {h^2 + r^2}\\ 17&= \sqrt {h^2 + 15^2}\\ 289&= h^2 + 225\\ h^2&=64\\ h& = 8. \end{align}\] Since the formula for the volume of a cone is \(\dfrac {1}{3} ×\pi ×r^2×h\), the volume of the cone is \[ \frac {1}{3}×3.14× 225 × 8= 1884 ~\big(\text{cm}^{2}\big). \ _\square\]

Find the volume of the following figure which depicts a cone and an hemisphere, up to \(2\) decimal places. In this figure, the shape of the base of the cone is circular and the whole flat part of the hemisphere exactly coincides with the base of the cone (in other words, the base of the cone and the flat part of the hemisphere are the same). Use \(\pi=\frac{22}{7}.\) \[\begin{align} (\text{Volume of cone}) & = \dfrac {1}{3} \pi r^2 h\\ & = \dfrac {1 × 22 × 36 × 8}{3 × 7}\\ & = \dfrac {6336}{21} = 301.71 \\\\ (\text{Volume of hemisphere}) & = \dfrac {2}{3} \pi r^3\\ & = \dfrac {2 × 22 × 216}{3 × 7}\\ & = \dfrac {9504}{21} = 452.57 \\\\ (\text{Total volume of figure}) & = (301.71 + 452.57) \\ & = 754.28.\ _\square \end{align} \]

Try the following problems.

Find the volume (in \(\text{cm}^3\)) of a cube of side length \(5\text{ cm} \).

A spherical balloon is inflated until its volume becomes 27 times its original volume. Which of the following is true?

Bob has a pipe with a diameter of \(\frac { 6 }{ \sqrt { \pi } }\text{ cm} \) and a length of \(3\text{ m}\). How much water could be in this pipe at any one time, in \(\text{cm}^3?\)

What is the volume of the octahedron inside this \(8 \text{ in}^3\) cube?

A sector with radius \(10\text{ cm}\) and central angle \(45^\circ\) is to be made into a right circular cone. Find the volume of the cone.

\[\] Details and Assumptions:

• The arc length of the sector is equal to the circumference of the base of the cone.

Three identical tanks are shown above. The spheres in a given tank are the same size and packed wall-to-wall. If the tanks are filled to the top with water, then which tank would contain the most water?

A chocolate shop sells its products in 3 different shapes: a cylindrical bar, a spherical ball, and a cone. These 3 shapes are of the same height and radius, as shown in the picture. Which of these choices would give you the most chocolate?

\[\text{ I. A full cylindrical bar } \hspace{.4cm} \text{ or } \hspace{.45cm} \text{ II. A ball plus a cone }\]

How many cubes measuring 2 units on one side must be added to a cube measuring 8 units on one side to form a cube measuring 12 units on one side?

This section involves a deeper understanding of volume and the formulas to find the volume. Here are a couple of worked out examples followed by several "Try It Yourself" problems:

\(12\) spheres of the same size are made from melting a solid cylinder of \(16\text{ cm}\) diameter and \(2\text{ cm}\) height. Find the diameter of each sphere. Use \(\pi=\frac{22}{7}.\) The volume of the cylinder is \[\pi× r^2 × h = \frac {22×8^2×2}{7}= \frac {2816}{7}.\] Let the radius of each sphere be \(r\text{ cm}.\) Then the volume of each sphere in \(\text{cm}^3\) is \[\dfrac {4×22×r^3}{3×7} = \dfrac{88×r^3}{21}.\] Since the number of spheres is \(\frac {\text{Volume of cylinder}}{\text {Volume of 1 sphere}},\) \[\begin{align} 12 &= \dfrac{2816×21}{7×88×r^3}\\ &= \dfrac {96}{r^3}\\ r^3 &= \dfrac {96}{12}\\ &= 8\\ \Rightarrow r &= 2. \end{align}\] Therefore, the diameter of each sphere is \[2\times r = 2\times 2 = 4 ~(\text{cm}). \ _\square\]

Find the volume of a hemispherical shell whose outer radius is \(7\text{ cm}\) and inner radius is \(3\text{ cm}\), up to \(2\) decimal places. We have \[\begin{align} (\text {Volume of inner hemisphere}) & = \dfrac{1}{2} × \dfrac{4}{3} × \pi × R^3\\ & = \dfrac {1 × 4 × 22 × 27}{2 × 3 × 7}\\ & = \dfrac {396}{7}\\ & = 56.57 ~\big(\text{cm}^{3}\big) \\\\ (\text {Volume of outer hemisphere}) & = \dfrac{1}{2} × \dfrac{4}{3} × \pi × r^3\\ & = \dfrac {1 × 4 × 22 × 343}{2 × 3 × 7}\\ & = \dfrac {2156}{7}\\ & = 718.66 ~\big(\text{cm}^{3}\big) \\\\ (\text{Volume of hemispherical shell}) & = (\text{V. of outer hemisphere}) - (\text{V. of inner hemisphere})\\ & = 718.66 - 56.57 \\ & = 662.09 ~\big(\text{cm}^{3}\big).\ _\square \end{align}\]

A student did an experiment using a cone, a sphere, and a cylinder each having the same radius and height. He started with the cylinder full of liquid and then poured it into the cone until the cone was full. Then, he began pouring the remaining liquid from the cylinder into the sphere. What was the result which he observed?

There are two identical right circular cones each of height \(2\text{ cm}.\) They are placed vertically, with their apex pointing downwards, and one cone is vertically above the other. At the start, the upper cone is full of water and the lower cone is empty.

Water drips down through a hole in the apex of the upper cone into the lower cone. When the height of water in the upper cone is \(1\text{ cm},\) what is the height of water in the lower cone (in \(\text{cm}\))?

On each face of a cuboid, the sum of its perimeter and its area is written. The numbers recorded this way are 16, 24, and 31, each written on a pair of opposite sides of the cuboid. The volume of the cuboid lies between \(\text{__________}.\)

A cube rests inside a sphere such that each vertex touches the sphere. The radius of the sphere is \(6 \text{ cm}.\) Determine the volume of the cube.

If the volume of the cube can be expressed in the form of \(a\sqrt{3} \text{ cm}^{3}\), find the value of \(a\).

A sphere has volume \(x \text{ m}^3 \) and surface area \(x \text{ m}^2 \). Keeping its diameter as body diagonal, a cube is made which has volume \(a \text{ m}^3 \) and surface area \(b \text{ m}^2 \). What is the ratio \(a:b?\)

Consider a glass in the shape of an inverted truncated right cone (i.e. frustrum). The radius of the base is 4, the radius of the top is 9, and the height is 7. There is enough water in the glass such that when it is tilted the water reaches from the tip of the base to the edge of the top. The proportion of the water in the cup as a ratio of the cup's volume can be expressed as the fraction \( \frac{m}{n} \), for relatively prime integers \(m\) and \(n\). Compute \(m+n\).

The square-based pyramid A is inscribed within a cube while the tetrahedral pyramid B has its sides equal to the square's diagonal (red) as shown.

Which pyramid has more volume?

Please remember this section contains highly advanced problems of volume. Here it goes:

Cube \(ABCDEFGH\), labeled as shown above, has edge length \(1\) and is cut by a plane passing through vertex \(D\) and the midpoints \(M\) and \(N\) of \(\overline{AB}\) and \(\overline{CG}\) respectively. The plane divides the cube into two solids. The volume of the larger of the two solids can be written in the form \(\frac{p}{q}\), where \(p\) and \(q\) are relatively prime positive integers. Find \(p+q\).

If the American NFL regulation football

has a tip-to-tip length of \(11\) inches and a largest round circumference of \(22\) in the middle, then the volume of the American football is \(\text{____________}.\)

Note: The American NFL regulation football is not an ellipsoid. The long cross-section consists of two circular arcs meeting at the tips. Don't use the volume formula for an ellipsoid.

Answer is in cubic inches.

Consider a solid formed by the intersection of three orthogonal cylinders, each of diameter \( D = 10 \).

What is the volume of this solid?

Consider a tetrahedron with side lengths \(2, 3, 3, 4, 5, 5\). The largest possible volume of this tetrahedron has the form \( \frac {a \sqrt{b}}{c}\), where \(b\) is an integer that's not divisible by the square of any prime, \(a\) and \(c\) are positive, coprime integers. What is the value of \(a+b+c\)?

Let there be a solid characterized by the equation \[{ \left( \frac { x }{ a } \right) }^{ 2.5 }+{ \left( \frac { y }{ b } \right) }^{ 2.5 } + { \left( \frac { z }{ c } \right) }^{ 2.5 }<1.\]

Calculate the volume of this solid if \(a = b =2\) and \(c = 3\).

• Surface Area

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VOLUME OF CYLINDER WORD PROBLEMS WORKSHEET

1. The cylindrical Giant Ocean Tank at the New England Aquarium in Boston is 24 feet deep and has a radius of 18.8 feet. Find the volume of the tank. Use the approximate of value of  π , that is 3.14 and round your answer to the nearest tenth if necessary.

2. A standard-size bass drum has a diameter of 22 inches  and is 18 inches deep. Find the volume of this drum. Use the approximate of value of    ∏ , that is 3.14 and round your answer to the nearest tenth if necessary.

3. A barrel of crude oil contains about 5.61 cubic feet of oil. How many barrels of oil are contained in 1 mile of a pipeline that has an inside diameter of 6 inches and is completely filled with oil ? How much is “1 mile” of oil in this pipeline worth at a price of $100 per barrel ?

4. A pan for baking French bread is shaped like half a cylinder as shown in the figure. Find the volume of uncooked dough that would fill this pan. Use the approximate of value of    ∏ , that is 3.14 and round your answer to the nearest tenth if necessary.

1. Answer :

Step 1 : 

Because the tank is in the shape of cylinder, we can use the formula of volume of a cylinder to find volume of the tank.

V  =   π r 2 h cubic units

Step 2 : 

Substitute  the given measures. 

V   ≈  3.14  · 18.8 2 · 24

(Here deep 24 feet is considered as height)

V  ≈  3.14 · 353.44 · 24

V  ≈  26635.2

So, the volume of the tank is about 26635.2 cubic feet.

2. Answer :

Usually the bass drum would be in the shape of cylinder. So, we can use the formula of volume of a cylinder, to find volume of the bass drum.

V  =   π r 2 h cubic units  -----(1)

To find the volume, we need the radius of the cylinder. But, the diameter is given, that is 22 in. So, find the radius. 

r  =  diameter / 2

r  =  22/2

r  =  11

Substitute  π    ≈  3.14,  r = 11 and h = 18  in (1) .

V  ≈  3.14  · 11 2  · 18

(Here deep 18 inches is considered as height)

V  ≈  3.14 · 121 · 18

V  ≈  6838.9

So, the volume of the bass drum is about 6838.9 cubic inches.

3. Answer :

Usually the pipe line would be in the shape of cylinder. So, we can use the formula of volume of a cylinder to find volume of the crude oil in the pipe line. 

To find the volume, we need the radius of the cylinder. But, the diameter is given, that is 6 in. So, find the radius. 

r  =  6/2

r  =  3 inches

Convert the inches into feet by multiplying 1/12.

Because, 

1 inch  =  1/12 feet

So, we have 

r  =  3 x 1/12 feet

r  =  1/4 feet

Convert the length of the pipeline from miles to feet.

1 mile  =  5280 feet

length  =  1 mile

length  =  1 x 5280 feet

length  =  5280 feet

Substitute  π    ≈  3.14,  r = 1/4 and h = 5280   in (1).

V   ≈  3.14  · (1/4) 2  · 5280

(Here , the length 5280 feet is considered as height)

V  ≈  3.14 · (1/16) · 5280

V  ≈  1036.2 cubic feet

To find how many  barrels of oil are contained in 1 mile of a pipeline, divide the volume of crude oil in the pipeline (1036.2 cu.ft) by 5.61.

Because a barrel of crude oil contains about 5.61 cubic feet of oil.

So, n umber of  barrels of oil are contained in 1 mile of a pipeline is 

=  1036.2 / 5.61

=  184.7

There are about 184.7  barrels of oil are contained in 1 mile of a pipeline.

Find the worth of  “1 mile” of oil in the pipeline at a price of $100 per barrel.

No. of barrels of oil in 1 mile of a pipeline  =  184.7  

So, the worth of  “1 mile” of oil in the pipeline is 

=  $100 x 184.7

=  $18,470

The worth of “1 mile” of oil in the pipeline at a price of $100 per barrel is about $18,470.

4. Answer :

Solution : 

Because the pan is shaped like half a cylinder, we  can use the formula of volume of a cylinder to find volume of  uncooked dough that would fill this pan

(Because the pan is shaped like half a cylinder,  1/2 is multiplied by the formula of volume of a cylinder)

To find the volume, we need the radius of the cylinder. But, the diameter is given, that is 3.5 in. So, find the radius. 

r  =  3.5/2

r  =  1.75

Substitute  π   ≈ 3.14,  r = 1.75 and h = 12  in (1) .

V  ≈   1/2   ·  3.14  · 1.75 2 · 12

V   ≈   1/2   ·  3.14  · 3.0625 · 12

V   ≈  57.7

So,  the volume of uncooked dough that would fill the pan is about 57.7 cu.inches.

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• Calculating Volume and Area

How to Calculate the Volume of a Cylinder

Last Updated: January 11, 2024 References

This article was co-authored by Grace Imson, MA . Grace Imson is a math teacher with over 40 years of teaching experience. Grace is currently a math instructor at the City College of San Francisco and was previously in the Math Department at Saint Louis University. She has taught math at the elementary, middle, high school, and college levels. She has an MA in Education, specializing in Administration and Supervision from Saint Louis University. There are 8 references cited in this article, which can be found at the bottom of the page. This article has been viewed 3,956,706 times.

A cylinder is a simple geometric shape with two equally-sized and parallel circular bases. Calculating the volume of a cylinder is simple once you know the formula. [1] X Research source

Help Finding the Volume of a Cylinder

Calculating the Volume of a Cylinder

• If you know the diameter of the circle, just divide it by 2. [3] X Research source
• If you know the circumference, then you can divide it by 2π to get the radius. [4] X Research source

• A = π x 1 2
• Since π is normally rounded to 3.14, you can say that the area of the circular base is 3.14 in. 2

• Always state your final answer in cubic units because volume is the measure of a three-dimensional space. [10] X Research source

Community Q&A

• Remember the diameter is the biggest chord in a circle or in a circumference, i.e. the biggest measurement you can get between two points in a circumference or in the circle within. The edge of the circle should meet the zero mark in your ruler/flex tape, and the biggest measurement you obtain without losing contact with your zero mark will be the diameter. [11] X Research source Thanks Helpful 1 Not Helpful 0
• Make up a few problems to practice so you know that you will get it right when you try it for real. Thanks Helpful 11 Not Helpful 3
• The volume of a cylinder is given by the formula V = πr 2 h, and π is about the equivalent of 22/7 or 3.14. Thanks Helpful 12 Not Helpful 10

Tips from our Readers

• To approximate the area of a circle, square its diameter, then multiply that by .7854. It's not precise, but it helps in a pinch.

You Might Also Like

• ↑ https://www.mathsisfun.com/definitions/cylinder.html
• ↑ Grace Imson, MA. Math Instructor, City College of San Francisco. Expert Interview. 1 November 2019.
• ↑ https://www.mathsisfun.com/definitions/radius.html
• ↑ https://www.mathsisfun.com/definitions/pi.html
• ↑ https://www.khanacademy.org/math/basic-geo/basic-geo-area-and-perimeter/area-circumference-circle/v/area-of-a-circle
• ↑ https://www.mathopenref.com/cylindervolume.html
• ↑ https://www.mathsisfun.com/definitions/volume.html
• ↑ https://www.cut-the-knot.org/pythagoras/Munching/DiameterChord.shtml

About This Article

1. Measure the circular base to get the diameter. 2. Divide the diameter by 2 to get the radius. 3. Calculate the area with the formula: A = πr^2, where r is the radius. 4. Measure the height of the cylinder. 5. Multiply the area by the height to get the Volume. Did this summary help you? Yes No

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• Math Article
• Volume Of A Cylinder

Volume of a Cylinder

The volume of a cylinder is the density of the cylinder which signifies the amount of material it can carry or how much amount of any material can be immersed in it. Cylinder’s volume is given by the formula,  πr 2 h, where r is the radius of the circular base and h is the height of the cylinder. The material could be a liquid quantity or any substance which can be filled in the cylinder uniformly. Check volume of shapes here.

Volume of cylinder has been explained in this article briefly along with solved examples for better understanding. In Mathematics , geometry is an important branch where we learn the shapes and their properties. Volume and surface area are the two important properties of any 3d shape.

The cylinder is a three-dimensional shape having a circular base. A cylinder can be seen as a set of circular disks that are stacked on one another. Now, think of a scenario where we need to calculate the amount of sugar that can be accommodated in a cylindrical box.

In other words, we mean to calculate the capacity or volume of this box. The capacity of a cylindrical box is basically equal to the volume of the cylinder involved. Thus, the volume of a three-dimensional shape is equal to the amount of space occupied by that shape.

Volume of a Cylinder Formula

A cylinder can be seen as a collection of multiple congruent disks, stacked one above the other. In order to calculate the space occupied by a cylinder, we calculate the space occupied by each disk and then add them up. Thus, the volume of the cylinder can be given by the product of the area of base and height.

For any cylinder with base radius ‘r’, and height ‘h’, the volume will be base times the height.

Therefore, the cylinder’s volume of base radius ‘r’, and height ‘h’ = (area of base) × height of the cylinder

Since the  base is the circle, it can be written as

Volume =  πr 2  × h

Therefore, the volume of a cylinder = πr 2 h cubic units.

Volume of Hollow Cylinder

In case of hollow cylinder, we measure two radius, one for inner circle and one for outer circle formed by the base of hollow cylinder. Suppose, r 1 and r 2  are the two radii of the given hollow cylinder with ‘h’ as the height, then the volume of this cylinder can be written as;

• V =  πh(r 1 2 – r 2 2 )

Surface Area of Cylinder

The amount of square units required to cover the surface of the cylinder is the surface area of the cylinder. The formula for the surface area of the cylinder is equal to the total surface area of the bases of the cylinder and surface area of its sides.

• A = 2πr 2 + 2πrh

Volume of Cylinder in Litres

When we find the volume of the cylinder in cubic centimetres, we can convert the value in litres by knowing the below conversion, i.e.,

1 Litre = 1000 cubic cm or cm 3 For example: If a cylindrical tube has a volume of 12 litres, then we can write the volume of the tube as 12 × 1000 cm 3 = 12,000 cm 3

Question 1: Calculate the volume of a given cylinder having height 20 cm and base radius of 14 cm. (Take pi = 22/7)

Height  = 20 cm

radius = 14 cm

we know that;

Volume, V = πr 2 h  cubic units

V=(22/7) × 14  × 14  × 20

V= 12320 cm 3

Therefore, the volume of a cylinder = 12320 cm 3

Question 2: Calculate the radius of the base of a cylindrical container of volume 440 cm 3 . Height of the cylindrical container is 35 cm. (Take pi = 22/7)

Volume = 440 cm 3

Height = 35 cm

We know from the formula of cylinder;

So, 440 =  (22/7) × r 2  × 35

r 2  = (440  × 7)/(22 × 35) = 3080/770 = 4

Therefore, r = 2 cm

Therefore, the radius of a cylinder = 2 cm.

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Frequently asked questions on volume of a cylinder, what is meant by the volume of a cylinder.

In geometry, the volume of a cylinder is defined as the capacity of the cylinder, which helps to find the amount of material that the cylinder can hold.

What is the formula for the volume of a cylinder?

The formula to calculate volume of a cylinder is given by the product of base area and its height. Since, the base area of a cylinder is circular, we can state that Volume of a cylinder = πr 2 h cubic units.

What is the volume of a hollow cylinder?

As we know, the hollow cylinder is a type of cylinder, which is empty from inside and it should possess some difference between the internal and the external radius. Thus, the amount of space occupied by the hollow cylinder in the three dimensional space is called the volume of a hollow cylinder.

How to calculate the volume of a hollow cylinder?

If R is the external radius and r is the internal radius, then the formula for calculating the cylinder’s volume is given by: V = π (R 2 – r 2 ) h cubic units.

What is the unit for the volume of a cylinder?

The volume of a cylinder is generally measured in cubic units, such as cubic centimeters (cm 3 ), cubic meters (m 3 ), cubic feet (ft 3 ) and so on.

How to find the volume of a cylinder if the diameter and height are given?

As we know, Diameter “d” = 2(Radius) = 2r. So, r = d/2 Now, substitute the value of “r” in the volume of cylinder formula, we get V = πr 2 h = π(d/2) 2 h V = (πd 2 h)/4 Hence, the volume of the cylinder is (πd 2 h)/4, if its diameter and height are given.

What will happen to the cylinder’s volume if its radius is doubled?

As we know, cylinder’s volume is directly proportional to the square of its radius. If the radius is doubled, (i.e., r = 2r), we get V = πr 2 h =π(2r) 2 h = 4πr 2 h. Hence, the cylinder’s volume becomes four times, when its radius is doubled.

What will happen to the cylinder’s volume if its radius is halved?

We know that, the volume of cylinder ∝ Radius2 Thus, if radius is halved, (i.e., r = r/2), we get V = π(r/2) 2 h = (πr 2 h)/4 Therefore, the cylinder’s volume becomes 1/4th, if its radius is halved.

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• Volume of Cylinders – Explanation & Examples

Volume of Cylinders – Explanation & Examples

This article will show you how to find the volume of a cylinder by using cylinder volume formula.

In geometry, a cylinder is a 3-dimensional shape with two equal, and parallel circles joined by a curved surface.

The distance between the circular faces of a cylinder is known as the height of a cylinder . The top and bottom of a cylinder are two congruent circles whose radius or diameter are denoted as ‘ r ’ and ‘ d ’, respectively.

How to Find the Volume of a Cylinder?

To calculate the volume of a cylinder, you need the radius or diameter of the circular base or top and a cylinder’s height.

The volume of a cylinder is equal to the product of the area of the circular base and the height of the cylinder. The volume of a cylinder is measured in cubic units.

Calculation of the volume of a cylinder is useful when designing cylindrical objects such as:

• Cylindrical water tanks or wells
• Perfume or chemical bottles
• Cylindrical containers and pipes
• Cylindrical flasks used in chemistry labs

Cylinder volume formula

The formula for the volume of a cylinder is given as:

Volume of a cylinder = πr 2 h cubic units

Where πr 2 = area of a circle;

r = radius of the circular base and;

h = height of a cylinder.

For a hollow cylinder, the volume formula is given as:

Volume of a cylinder = πh (r 1 2  – r 2 2 )

Where, r 1  = external radius and r 2 = internal radius of a cylinder.

The difference of the external and internal radius forms the wall thickness of a cylinder i.e.

Wall thickness of a cylinder = r 1 – r 2

Let’s solve a few example problems about the volume of cylinders.

The diameter and height of a cylinder are 28 cm and 10 cm, respectively. What is the volume of the cylinder?

The radius is half of the diameter.

Diameter = 28 cm ⇒ radius = 28/2

Height = 10 cm

By the cylinder volume formula;

volume = πr 2 h

= 3.14 x 14 x 14 x 10

= 6154.4 cm 3

So, the volume of the cylinder is 6154.4 cm 3

The depth of water in a cylindrical tank is 8 feet. Suppose the radius and height of the tank are 5 feet and 11.5 feet, respectively. Find the volume of water required to fill the tank to the brim.

First calculate the volume of the cylindrical tank

Volume = 3.14 x 5 x 5 x 11.5

= 902.75 cubic feet

Volume of water in the tank = 3.14 x 5 x 5 x 8

= 628 cubic feet.

The volume of water required to fill the tank = 902.75 – 628 cubic feet

= 274.75 cubic feet.

The volume of a cylinder is 440 m 3 , and the radius of the base is 2 m. Calculate the height of the tank.

Volume of a cylinder = πr 2 h

440 m 3 = 3.14 x 2 x 2 x h

440 = 12.56h

By dividing 12.56 on both sides, we get

Therefore, the height of the tank is 35 meters.

The radius and height of a cylindrical water tank are 10 cm and 14 cm, respectively. Find the volume of the tank in liters.

= 3.14 x 10 x 10 x 14

= 4396 cm 3

Given, 1 Liter = 1000 cubic centimeter (cm 3 )

Therefore, divide 4396 by 1000 to get

Volume = 4.396 liters

The external radius of a plastic pipe is 240 mm, and the internal radius is 200 mm. If the pipe’s length is 100 mm, find the volume of material used to make the pipe.

A pipe is an example of a hollow cylinder, so we have

= 3.14 x 100 x (240 2 – 200 2 )

= 3.14 x 100 x 17600

= 5.5264 x 10 6 mm 3 .

A cylindrical solid block of a metal is to be melted to form cubes of edge 20 mm. Suppose the radius and length of the cylindrical block are 100 mm and 490 mm, respectively. Find the number of cubes to be formed.

Calculate the volume of the cylindrical block

volume = 3.14 x 100 x 100 x 490

= 1.5386 x 10 7 mm 3

Volume of the cube = 20 x 20 x 20

= 8000 mm 3

The number of cubes = volume of the cylindrical block/volume of the cube

= 1.5386 x 10 7 mm 3 / 8000 mm 3

= 1923 cubes.

Find the radius of a cylinder with the same height and volume as a cube of sides 4 ft.

Height of cube = height of cylinder = 4 feet and,

volume of the cube = volume of cylinder

4 x 4 x 4 = 64 cubic feet

But volume of a cylinder = πr 2 h

3.14 x r 2 x 4 = 64 cubic feet

12.56r 2 =64

Divide both sides by 12.56

r 2 = 5.1 feet.

Therefore, the radius of the cylinder will be 1.72 feet.

A solid hexagonal prism has a base length of 5 cm and a height of 12 cm. Find the height of a cylinder with the same volume as the prism. Take the radius of the cylinder to be 5 cm.

The formula for the volume of a prism is given as;

Volume of a prism = (h)(n) (s 2 )/ [4 tan (180/n)]

where, n = number of sides

s = base length of a prism

h = height of a prism

Volume = (12) (6) (5 2 )/ (4tan 180/6)

=1800/2.3094

=779.42 cm 3

779.42 =3.14 x 5 x 5 x h

h = 9.93 cm.

So, the height of the cylinder will be 9.93 cm.

Practice Questions

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Formula Volume of a Cylinder

How to find the Volume of a Cylinder

This page examines the properties of a right circular cylinder . A cylinder has a radius (r) and a height (h) (see picture below).

Cylinder Volume Formula

Practice Problems on Area of a Cylinder

What is the volume of the cylinder with a radius of 2 and a height of 6?

Use the formula for the volume of a cylinder as shown below.

• Volume = Π *(r) 2 (h)
• Volume = Π *(2) 2 (6)

What is the volume of the cylinder with a radius of 3 and a height of 5?

• Volume = Π *(3) 2 (5)

What is the area of the cylinder with a radius of 6 and a height of 7?

Use the area of a cylinder formula .

• Volume = Π *(6) 2 (7)

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Volume of a Cylinder Calculator

Use this cylinder volume calculator to easily calculate the volume of a cylinder from its base radius and height in any metric: mm, cm, meters, km, inches, feet, yards, miles...

    Calculation results

Related calculators.

• Volume of a cylinder formula
• How to calculate the volume of a cylinder?
• Example: find the volume of a cylinder
• Practical applications

    Volume of a cylinder formula

The formula for the volume of a cylinder is height x π x (diameter / 2) 2 , where (diameter / 2) is the radius of the base (d = 2 x r), so another way to write it is height x π x radius 2 . Visual in the figure below:

First, measure the diameter of the base (usually easier than measuring the radius), then measure the height of the cylinder. To do the calculation properly, you must have the two measurements in the same length units. The result from our volume of a cylinder calculator is always in cubic units, based on the input unit: in 3 , ft 3 , yd 3 , cm 3 , m 3 , km 3 , and so on.

    How to calculate the volume of a cylinder?

One can think of a cylinder as a series of circles stacked one upon another. The height of the cylinder gives us the depth of stacking, while the area of the base gives us the area of each circular slice. Multiplying the area of the slice by the depth of the stack is an easy way to conceptualize the way for calculating the volume of a cylinder. Since in practical situations it is easier to measure the diameter (of a tube, a round steel bar, a cable, etc.) than it is to measure the radius, and on most technical schemes it is the diameter which is given, our cylinder volume calculator accepts the diameter as an input. If you have the radius instead, just multiply it by two.

Using the formula and doing the calculations by hand can be difficult due to the value of the π constant: ~3.14159, which can be hard to work with, so a volume of a cylinder calculator significantly simplifies the task.

    Example: find the volume of a cylinder

Applying the volume formulas is easy provided the cylinder height is known and one of the following is also given: the radius, the diameter, or the area of the base. For example, if the height and area are given to be 5 feet and 20 square feet, the volume is just a multiplication of the two: 5 x 20 = 100 cubic feet.

If the radius is given, using the second equation above can give us the cylinder volume with a few additional steps. For example, the height is 10 inches and the radius is 2 inches. First, we find the area by 3.14159 x 2 2 = 3.14159 x 4 = 12.574, then multiply that by 10 to get 125.74 cubic inches of volume. Using a higher level of precision for π results in more accurate results, e.g. our calculator computes the volume of this cylinder as 125.6637 cu in.

    Practical applications

The cylinder is one of the most widely used body shapes in engineering and architecture: from tunnels, covered walkways to tubes, cables, round bars, the cylinders and pistons in your car's engine - cylinders are everywhere. Calculating cylinder volume is useful when you want to know its displacement, or how much liquid or gas you need to fill it, e.g. how much water you need to fill your jacuzzi. Cylindrical aquariums are also fairly common, so are cylindrical artificial lakes, fountains, gas containers / tanks, etc.

Cite this calculator & page

If you'd like to cite this online calculator resource and information as provided on the page, you can use the following citation: Georgiev G.Z., "Volume of a Cylinder Calculator" , [online] Available at: https://www.gigacalculator.com/calculators/volume-of-cylinder-calculator.php URL [Accessed Date: 27 Mar, 2024].

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Volume of a Cylinder

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Volume of Cylinders

Subject: Mathematics

Age range: 14-16

Resource type: Lesson (complete)

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One FULL LESSON on finding the volume of cylinders. This lesson follows on from volume of prisms.

Contents of download:

• Clicker version : Normal PowerPoint lesson with which you can use a clicker / mouse / keyboard to continue animations and show solutions.
• Worksheets (including example and extension).

We are learning about: The volume of a cylinder We are learning to: Calculate the volume of a cylinder.

Differentiated objectives:

• Developing learners will be able to calculate the volume of a cylinder.
• Secure learners will be able to find a missing length in a cylinder given its volume.
• Excelling learners will be able to solve unfamiliar problems using their knowledge of calculating the volume of a cylinder.

Main: Walkthrough examples followed by practice questions on worksheets. Starts with basic calculating the volume moving on to finding missing lengths of a cylinder. All solutions given on PPT and in worksheet format.

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Course: 8th grade   >   Unit 5

• Cylinder volume & surface area
• Volume of cylinders
• Volume of a sphere
• Volume of spheres
• Volume of a cone
• Volume of cones

Volume of cylinders, spheres, and cones word problems

• Geometry: FAQ
• Your answer should be
• an integer, like 6 ‍  
• a simplified proper fraction, like 3 / 5 ‍  
• a simplified improper fraction, like 7 / 4 ‍  
• a mixed number, like 1   3 / 4 ‍  
• an exact decimal, like 0.75 ‍  
• a multiple of pi, like 12   pi ‍   or 2 / 3   pi ‍