Step by step
The question
Question: a sector has radius 10 cm and angle 72°: 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 around the middle is 360°.
A bigger angle cuts a bigger slice.
The slice is 72° of the 360°: 72/360.
To make it simpler: 72 goes into 360: 72 × 5 = 360.
So 72 goes into both.
So we divide the top and the bottom by 72.
That is 1/5 of the circle.
2 Whole circle
The whole edge, the circumference, is 2 times π times r.
2 times 10 is 20.
So it is 20π.
3 Take the part
The slice is 1/5 of the whole circle.
"Of" means times.
Cut the whole into 5 equal parts.
One part is 20 divided by 5: 4.
The π stays.
So it is 4π.
With a calculator, π is 3.14159 and more.
4 times π is about 12.57, to 2 decimal places.
So the arc is 4π, about 12.57 cm.
4 Check
Let's check: 5 slices like this make the whole circle.
5 times 4π is 20π, the whole edge.
So it is right!
Let's look back.
First: what part of the circle.
Then: whole circle.
Then: take the part.
Last: check.