Volume of a Cylinder Calculator

Welcome to our Volume of a Cylinder Calculator page.

We explain how to find the volume of a right circular cylinder and provide a quick calculator to work it out for you, step-by-step.

There are also some worked examples and some worksheets for you to practice this skill.

Volume of a Cylinder Calculator

This calculator finds the volume of a right circular cylinder when the radius (or diameter) and height are known.

Volume of a Cylinder Calculator

volume of a cylinder labelled image


Answer1


Answer2

 
 

How the Volume of a Cylinder Calculator Works

  1. Select if you want to use the radius or diameter (default is radius).
  2. For the value, you can choose a whole number, decimal or fraction.
    • You can type a fraction by typing the numerator then '/' then the denominator.
    • You can type a mixed number by typing the whole-number part, then a space then the fraction part.
    • Examples: 2 1/2 (two and one-half); 3 4/5 (three and four-fifths); 7 1/3 (seven and one-third).
  3. Choose your units of measurement (default is none)
  4. Choose your desired accuracy (default is 2 decimal places)
  5. Click the Find Volume button
  6. You will be given two answers for the area, one in terms of Pi (π) and the other answer as a decimal value.

Volume of a Cylinder Formula

volume of a cylinder formula image

The volume of a right circular cylinder is: \[ V = \pi r^2 h \]

where r is the radius of the circle and h is the height of the cylinder.

How to Find the Volume of a Cylinder Support

If you would like to see where the formula comes from, then we hope you will find the explanation below useful.

We going to look at a closed right circular cylinder and work out the volume.

cylinder image labelled

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

To find the amount of space inside the cylinder, we need to find the area of the circular base and multiply this amount by the height.

The area of the circular base of the cylinder is: \[ A = \pi r^2 \] where A is the area and r is the radius of the circle.

The height of the cylinder is h.

This means that the volume of the cylinder is: \[ V = \pi r^2 h \]

Volume of a Cylinder Examples

Volume of a Cylinder Example 1

Find the volume of the cylinder below to 1 decimal place.

volume of a cylinder example 1

The formula for the volume of a cylinder is: \[ V = \pi r^2 h \]

If we substitute the values of the radius and height into this equation, we get: \[ V = \pi \cdot 4^2 \cdot 6 = \pi \cdot 16 \cdot 6 = 96 \pi \]

This gives us a final answer of: \[ V =301.6 \;\ cm^3 \; to \; 1 \; decimal \; place \]


Volume of a Cylinder Example 2

Find the volume of the cylinder below to 1 decimal place.

volume of a cylinder example 2

The formula for the volume of a cylinder is: \[ V = \pi r^2 h \]

As the cylinder is lying on its side, the actual 'height' of the cylinder is 6 ft and the radius is 2 ½ ft

If we substitute the values of the radius and height into this equation, we get: \[ V = \pi \cdot (2 {1 \over 2})^2 \cdot 6 = \pi \cdot {25 \over 4} \cdot 6 = {75 \over 2} \pi \]

This gives us a final answer of: \[ V = 117.8 \;\ ft^3 \; to \; 1 \; decimal \; place \]


Volume of a Cylinder Example 3

Find the volume of the cylinder below to 2 decimal places.

volume of a cylinder example 3

We have been given the diameter instead of the radius. To find the radius, we just need to halve the diameter.

So the radius of the circular base is: \[ r = 9.4 \div 2 = 4.7 m \]

The formula for the volume of a cylinder is: \[ V = \pi r^2 h \]

If we substitute the values of the radius and height into this equation, we get: \[ V = \pi \cdot 4.7^2 \cdot 5.7 = \pi \cdot 22.09 \cdot 5.7 = 125.913 \pi \]

This gives us a final answer of: \[ V = 395.57 \;\ m^3 \; to \; 2 \; decimal \; places \]


Volume of a Cylinder Worksheets

We have created two worksheets to help you practice this skill.

The first sheet involves working out the volume of a range of cylinders where the radius is given.

The second sheet involves working out the volume of cylinders where either the radius or diameter is given.

You can check your answers to the questions on the sheets using our volume of a cylinder calculator.

More Recommended Math Resources

Take a look at some more of our worksheets similar to these.

Volume of a Pipe Calculator

This calculator works in the same way as the one above, but finds the volume of a pipe (which is basically an open cylinder).

The main difference is that this calculator can cope with different units of measure and you can convert the volume into liters, gallons, or fluid ounces, as well as cm3, m3, etc

Surface Area of a Cylinder Calculator

This calculator works in the same way as the one above, but finds the surface area of the cylinder instead of the volume.

More Circle Worksheets and Support Pages

More Area & Volume Calculators

We have a range of other area calculators to help you find the area of a range of different 2d and 3d shapes.

More Area Support and Resources

We have a range of other area worksheets and support pages for a range of different 2d shapes.

Looking for more math calculators?

We have a wide range of free math calculators to help you.

Most of our calculators show you their working out so that you can see exactly what they have done to get the answer.

Our calculator hub page contains links to all of our calculators!

 

How to Print or Save these sheets

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Need help with printing or saving?
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How to Print or Save these sheets

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Need help with printing or saving?
Follow these 3 easy steps to get your worksheets printed out perfectly!

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