Step by step
The question
Question: a sector has radius 6 cm and angle 60°: find the arc length.
The arc is the curved part of the edge of the slice.
1 What part of the circle
A whole turn is 360°.
The slice is 60° out of 360°: that is 1/6 of the circle.
part = 60°360° = 16
60 and 360 can both be divided by 60.
60 ÷ 60 = 1, 360 ÷ 60 = 6
2 Whole circle
The whole edge, the circumference, is 2 π r: 2 times π times 6 is 12π.
circumference = 2 × π × 6 = 12π
3 Take the part
Now 1/6 of 12π: 2π.
arc length = 16 × 12π = 2π
In π that is 2π.
As a decimal: about 6.28 cm, to 2 decimal places.
≈ 2π ≈ 6.28 cm
4 Check
Let's check: 6 slices like this make the whole circle.
6 times 2π is 12π, the whole edge.
So it is right!
6 slices: 6 × 2π = 12π
Let's look back.
First: what part of the circle.
Then: whole circle.
Then: take the part.
Last: check.
Answer
≈ 2π ≈ 6.28 cm