Surface area of hemisphere radius 3

Step by step

The question

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

1 Count the parts

A hemisphere has a curved part on top and a flat circle at the bottom.

2 The curved part

The skin of a whole ball is 4 circles.

The curved part is half of it: 2 circles.

π is a special number for circles.

It is about 3.14.

So the curved part is 2 × π × r².

Now put the numbers in: r = 3.

3² means 3 times 3.

That is 9.

So curved = 2 × π × 9.

2 times 9 is 18.

So the curved part is 18π.

3 The flat circle

The flat circle at the bottom has radius 3.

A circle is π × r².

Now put the numbers in: r = 3.

3² is 9, as before.

So the flat circle is 9π.

4 Add the parts

Now we add the curved part and the flat circle.

18 plus 9 is 27.

So S = 27π.

We keep π in the answer.

That is the exact answer.

5 About how much

To see about how much, put 3.14 for π.

27 times 3.14 is 84.78.

So the surface area is about 84.78 square units.

Let's look back.

First: count the parts.

Then: the curved part.

Then: the flat circle.

Then: add the parts.

Last: about how much.