Sector radius 10, area 25π, find the angle

Step by step

The question

Question: a sector has radius 10 and area 25π: find the angle of the sector.

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

1 Whole circle

The whole circle has area π r squared: 100π.

2 What part of the circle

The sector is 25π out of 100π.

The π's cancel: 1/4 of the circle.

3 Find the angle

The whole turn is 360°.

1/4 of 360° is 90°.

Careful!

The slice is the same part of the area and of the angle.

4 Check

Let's check: 90 out of 360 is 1/4 too.

So it is right!

Let's look back.

First: whole circle.

Then: what part of the circle.

Then: find the angle.

Last: check.