Area of square 10 with a circle radius 3 cut out Step by Step

Step by step

The question

Question: find the area of this shape: a 10 square with a circle of radius 3 cut out.

1 The whole and the hole

The whole shape would be a 10 square.

A circle is cut out.

That part is not there any more.

So we take it away.

2 Area of each part

The whole square: length times width.

10 times 10 is 100.

whole = 10 × 10 = 100

The hole is a circle: π times r squared.

hole = π × 3²

3² means 3 times 3.

That is 9.

3² = 3 × 3 = 9

π times 9 is written 9π.

hole = 9π

3 Take away the hole

The area is the whole, take away the hole: 100 − 9π.

We keep π in the answer.

That is the exact answer.

A = 100 − 9π

4 About how much

To see about how much, put 3.14 for π.

A ≈ 100 − 9 × 3.14

9 times 3.14 is 28.26.

A ≈ 100 − 28.26

100 minus 28.26 is 71.74.

So the area is about 71.74 square units.

A ≈ 71.74

5 Check

Let's check: put the hole back.

That is about 28.26.

We should get the whole square.

71.74 + 28.26 = 100

We get 100, the whole square.

So the area is right!

Let's look back.

First: the whole and the hole.

Then: area of each part.

Then: take away the hole.

Then: about how much.

Last: check.

Answer