A cylinder has radius 3 cm and height 12 cm. Work out its volume.

Step by step

The question

Question: find the volume of a cylinder with radius 3 cm and height 12 cm.

1 Circle times height

The top is a circle.

A circle's area is π × r².

π is a special number for circles: the way round is about 3.14 times the way across.

Like a box: one layer, times the number of layers.

Here the bottom layer is the circle.

Each 1 cm up is one more layer: 12 layers.

So the volume is circle area times height: V = π × r² × h.

Now put the numbers in: r = 3 and h = 12.

3² means 3 times 3.

That is 9.

So V = π × 9 × 12.

9 times 12 is 108.

So V = 108π.

We keep π in the answer.

That is the exact answer.

2 About how much

To see about how much, put 3.14 for π.

108 times 3.14 is 339.12.

So the volume is about 339.12 cm³.

Let's look back.

First: circle times height.

Last: about how much.