# Volume of a cylinder

In this lesson, you'll learn how to calculate the volume of a cylinder.

## What is a cylinder?

It's a three dimensional shape comprising two equal circular ends and a
curved surface.

And the volume of a cylinder?

This is the amount of three dimensional space occupied by the cylinder.

## Volume of cylinder formula

**Cylinder volume = area of one of circular ends x height**

The area of each cylinder end is πr² (where π = pi and r = radius of circle) - see also area of a circle.

So if h = cylinder height, the formula becomes

where Vcylinder = volume of cylinder.

*Have you noticed **the volume of a cone (**πr**²h) **is three times the volume of a cylinder (1/3 x **πr**²h)?** Given the same radius and height, you can fit three cones into one cylinder! *

Worked example

What's the volume of a cylinder with radius (r) 3cm and height (h) 4cm (where cm = centimeters)?

Vcylinder

= πr²h

= π x 3² x 4

= 113.1cm³ (cubic centimeters) to 1 d.p. (one decimal place)

*Square the radius r on your calculator using **x**²**. *In order, enter *pi sign (**π), multiply sign (x), 3, **x**², multiply sign (x), 4, equals sign (=). The display should show 113.0973355 which is 113.1 to 1 d.p. You may need to use a shift or 2nd function button on your calculator to access **x**² and* *π.*

## Now consider a cylinder with radius (r) 6m and height (h) 8m (where m = meters)

Vcylinder

= πr²h

= π x 6² x 8

= 904.78m³ (cubic meters) to 2 d.p. (two decimal places)

*Grab your calculator again - press** pi sign (**π), 6,** **x**²**, multiply sign (x), 8, equals sign (=).*

## Over to you!

Use different values for radius (r) and height (h) to calculate the volumes of cylinders of varying size.

*Your answers should include appropriate units (for example, cubic centimeters cm³, cubic meters m³), together with the number of decimal places (d.p.) to which you are rounding.*

Once you feel confident, move on to the next lesson - how to work out the surface area of a cylinder.

For further related lessons click:

Volume of a cone

Surface area of a cone

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Volume of a cylinder