# What is the formula for finding the volume (capacity) of a cylinder or tin?

## Volume Of a Cylinder Video

The volume of a cylinder can be found by working out the area of the circle at the end of the cylinder using A = πr² (also referred as the cross-sectional area) and multiply this answer by the length of the cylinder. Therefore:

Volume = Cross sectional area × Length

V = πr² × l

V = πlr²

So if you have the radius and length of the cylinder then all you need to is substitute these into the formula V = πlr².

**Example 1**

Work out the volume of the cylinder below:

Here the radius of the cylinder is 5cm and the length of the cylinder is 12cm:

So r = 5cm and l = 12cm

First work out the area of the circle:

A = πr²

A = π × 5²

A= 78.5...cm²

Leave this answer on your calculator and multiply it by the length to give the volume:

V = 78.5... × 12

= 942 cm³ to the nearest whole unit

Alternatively, you can substitute r = 5 and l = 12 directly into V = πlr²

V = πlr²

V = π × 12 × 5²

V = 942 cm³

**Example 2**

Work out the volume of the cylinder below:

Here the diameter of the cylinder is 22cm and the length of the cylinder is 40cm.

Notice that you are given the diameter of the circle and not the radius of the circle so you need to halve the diameter to give the radius:

So r = 11cm and l = 40cm

First work out the area of the circle:

A = πr²

A = π × 11²

A= 380.1...cm²

Leave this answer on your calculator and multiply it by the length to give the volume:

V = 380.1... × 40

= 15205 cm³ to the nearest whole unit

Alternatively, you can substitute r = 11 and l = 40 directly into V = πlr²

V = πlr²

V = π × 40 × 11²

V = 15205 cm³

**Example 3**

A tin of soup has a radius of 2 inches and a height of 5 inches. Work out the volume of soup in the tin.

Here r = 2 and l = 5. This time let’s just substitute r = 2 and l = 5 into V = πlr²:

V = πlr²

V = π × 5 × 2²

V = 62.8 cm³ rounded to the nearest tenth.

## More by this Author

- 26
A compound shape is a shape that is made up from other simple shapes. In this article we will be working out the area of a L shape (made up from 2 rectangles). To find the area of a compound shape, follow these simple...

- 14
The nth term of a number sequence is a formula that gives you the values in the numbers sequence from the position number (some people call it the position to term rule). Example 1 Find the nth term of this...

- 0
The surface area of a triangular prism can be found in the same way as any other type of prism. All you need to do is calculate the total area of all of the faces. A triangular prism has 5 faces, 3 being rectangular and...

## 1 comment

Some excellent calculations explained clearly. Having the examples fleshes it out. Voting this Up and Useful.