Question

How do you find the area of a circle when given the area of a sector?

Answer 1

The problem will undoubtedly give you more information about the sector. A sector of a circle is like a slice of a pie, and its area will depend on the angle between the 2 "sides" of the pie.

If they tell you that the area of a 60 degree sector is 14 square cm., think about what fraction of the "whole pie" this "slice" is. A circle is a 360 degree arc, so 60 degrees is (60/360) or (1/6) of a whole circle. You would have to multiply the sector area by 6 to get the area of the whole circle.

They might tell you that a 9 degree sector has an area of 38 square cm., this is (9/360) of a whole circle, so you need to multiply the sector area by (360/9) = 40. So 38(40) = 1520 square cm. for the whole circle.

Let's say they tell you that an x degree sector has an area of 20 square cm., this is (x/360) of a whole circle, so you need to multiply the sector area by (360/x). 20(360/x) = 720/x square cm. for the circle.