Step by step
The question
Question: a sector has radius 6 and area 12π: 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: 36π.
whole area = π × 6² = 36π
2 What part of the circle
The sector is 12π out of 36π.
The π's cancel: 1/3 of the circle.
part = 12π36π = 13
3 Find the angle
The whole turn is 360°.
1/3 of 360° is 120°.
angle = 13 × 360° = 120°
Careful!
The slice is the same part of the area and of the angle.
Careful: the part of the circle = the part of 360°
4 Check
Let's check: 120 out of 360 is 1/3 too.
So it is right!
120°360° = 13
Let's look back.
First: whole circle.
Then: what part of the circle.
Then: find the angle.
Last: check.
Answer
Careful: the part of the circle = the part of 360°