Step by step
The question
Question: a sector has radius 8 cm and angle 45°: 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 45° of the 360°: 45/360.
To make it simpler: 45 goes into 360: 45 × 8 = 360.
So 45 goes into both.
So we divide the top and the bottom by 45.
That is 1/8 of the circle.
2 Whole circle
The whole edge, the circumference, is 2 times π times r.
2 times 8 is 16.
So it is 16π.
3 Take the part
The slice is 1/8 of the whole circle.
"Of" means times.
Cut the whole into 8 equal parts.
One part is 16 divided by 8: 2.
The π stays.
So it is 2π.
With a calculator, π is 3.14159 and more.
2 times π is about 6.28, to 2 decimal places.
So the arc is 2π, about 6.28 cm.
4 Check
Let's check: 8 slices like this make the whole circle.
8 times 2π is 16π, 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.