Surface area of hemisphere diameter 10

Step by step

The question

Question: find the surface area of a hemisphere (half a ball) with diameter 10.

1 Find the radius

The diameter goes all the way across the circle.

The radius is half of it.

Half of 10 is 10 divided by 2.

10 divided by 2 is 5.

So r = 5.

2 Count the parts

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

3 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 = 5.

5² means 5 times 5.

That is 25.

So curved = 2 × π × 25.

2 times 25 is 50.

So the curved part is 50π.

4 The flat circle

The flat circle at the bottom has radius 5.

A circle is π × r².

Now put the numbers in: r = 5.

5² is 25, as before.

So the flat circle is 25π.

5 Add the parts

Now we add the curved part and the flat circle.

50 plus 25 is 75.

So S = 75π.

We keep π in the answer.

That is the exact answer.

6 About how much

To see about how much, put 3.14 for π.

75 times 3.14 is 235.5.

So the surface area is about 235.5 square units.

Let's look back.

First: find the radius.

Then: count the parts.

Then: the curved part.

Then: the flat circle.

Then: add the parts.

Last: about how much.