Math CentralQuandaries & Queries


Question from erica, a student:

What is the perimeter of a sector if the radius is 18 and the middle arc is 150 degrees?

Hi Erica,

The circumference (perimeter) of a circle is given by

circumference = 2 π r

where r is the radius and π is approximately 3.1426. You have a radius of r units so you can find the circumference.

Your sector is only a fraction of the circle, in fact it is 150/360 of the circle. The arc of the sector is only a fraction of the perimeter of the circle. In fact it is 150/360 of the perimeter. The sector is shaped like a piece of pie, the perimeter is the length of the arc plus twice the radius.

I hope this helps,

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