Step by step
The question
Question: a sector has radius 9 and arc length 3π: find the angle of the sector.
The arc is the curved part of the edge of the slice.
1 Whole circle
The whole edge is 2 π r: 18π.
whole edge = 2 × π × 9 = 18π
2 What part of the circle
The sector is 3π out of 18π.
The π's cancel: 1/6 of the circle.
part = 3π18π = 16
3 Find the angle
The whole turn is 360°.
1/6 of 360° is 60°.
angle = 16 × 360° = 60°
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: 60 out of 360 is 1/6 too.
So it is right!
60°360° = 16
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°