Step by step
The question
Question: a sector has radius 10 cm and angle 36°: 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 36° out of 360°: that is 1/10 of the circle.
part = 36°360° = 110
36 and 360 can both be divided by 36.
36 ÷ 36 = 1, 360 ÷ 36 = 10
2 Whole circle
The whole edge, the circumference, is 2 π r: 2 times π times 10 is 20π.
circumference = 2 × π × 10 = 20π
3 Take the part
Now 1/10 of 20π: 2π.
arc length = 110 × 20π = 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: 10 slices like this make the whole circle.
10 times 2π is 20π, the whole edge.
So it is right!
10 slices: 10 × 2π = 20π
Let's look back.
First: what part of the circle.
Then: whole circle.
Then: take the part.
Last: check.
Answer
≈ 2π ≈ 6.28 cm