Sector radius 8 cm, angle 45°, find the area

Step by step

The question

Question: a sector has radius 8 cm and angle 45°: find the area of the sector.

A sector is a slice of the circle, like a slice of pizza.

1 What part of the circle

A whole turn is 360°.

The slice is 45° out of 360°: that is 1/8 of the circle.

45 and 360 can both be divided by 45.

2 Whole circle

The area of the whole circle is π r squared: π times 64 is 64π.

Careful!

Area uses r squared: 8 times 8.

Not 2 r.

3 Take the part

Now 1/8 of 64π: 8π.

In π that is 8π.

As a decimal: about 25.13 cm², to 2 decimal places.

4 Check

Let's check: 8 slices like this make the whole circle.

8 times 8π is 64π, the whole area.

So it is right!

Let's look back.

First: what part of the circle.

Then: whole circle.

Then: take the part.

Last: check.