Sector radius 7 cm, angle 60°, find the perimeter

Step by step

The question

Question: a sector has radius 7 cm and angle 60°: 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 60° out of 360°: that is 1/6 of the circle.

60 and 360 can both be divided by 60.

2 Whole circle

The whole edge, the circumference, is 2 π r: 2 times π times 7 is 14π.

3 Take the part

Now 1/6 of 14π: 7π over 3.

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, 7 and 7.

That is 7π over 3 plus 14, about 21.33 cm.

5 Check

Let's check: 6 slices like this make the whole circle.

6 times 7π over 3 is 14π, the whole edge.

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.