Sector radius 4 cm, angle 90°, find the arc length

Step by step

The question

Question: a sector has radius 4 cm and angle 90°: 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 90° out of 360°: that is 1/4 of the circle.

90 and 360 can both be divided by 90.

2 Whole circle

The whole edge, the circumference, is 2 π r: 2 times π times 4 is 8π.

3 Take the part

Now 1/4 of 8π: 2π.

In π that is 2π.

As a decimal: about 6.28 cm, to 2 decimal places.

4 Check

Let's check: 4 slices like this make the whole circle.

4 times 2π is 8π, 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.