Sector radius 15 cm, angle 240°, find the perimeter

Step by step

The question

Question: a sector has radius 15 cm and angle 240°: find the perimeter of the sector.

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 240° out of 360°: that is 2/3 of the circle.

240 and 360 can both be divided by 120.

2 Whole circle

The whole edge, the circumference, is 2 π r: 2 times π times 15 is 30π.

3 Take the part

Now 2/3 of 30π: 20π.

Careful!

The perimeter is all the way round the slice: the arc and the two straight radii.

4 Add the two radii

All the way round: the arc plus two radii, 15 and 15.

That is 20π plus 30, about 92.83 cm.

5 Check

Let's check: the whole is 3/2 times the part: 30π again.

So it is right!

Let's look back.

First: what part of the circle.

Then: whole circle.

Then: take the part.

Then: add the two radii.

Last: check.