Volume of hemisphere radius 3

Step by step

The question

Question: find the volume of a hemisphere (half a ball) with radius 3.

1 Half of a ball

A hemisphere is half of a ball.

A whole ball is 4/3 × π × r³.

π is a special number for circles.

It is about 3.14.

So the hemisphere is half of it: V = ½ × 4/3 × π × r³.

Half of 4 thirds is 2 thirds.

So V = 2/3 × π × r³.

Now put the numbers in: r = 3.

3³ means 3 times 3 times 3.

That is 27.

So V = 2/3 × π × 27.

Keep the numbers small: divide 27 by 3 first.

27 divided by 3 is 9.

So V = 2 × π × 9.

2 times 9 is 18.

So V = 18π.

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.

18 times 3.14 is 56.52.

So the volume is about 56.52 cubic units.

Let's look back.

First: half of a ball.

Last: about how much.