Question

Suppose that circles A and B have a central angle measuring 40°. Additionally, circle A has a radius of 5 2 ft and the radius of circle B is 9 2 ft. If the measure of the sector for circle A is 25 36 π ft2, what is the measure of the sector for circle B?

Answer 1

It is 9/4π ft².

Since the central angle is 40°, this is 40/360 = 1/9 of the circle.

The area of the circle is given by A=πr²; since r=9/2, we have
A=π(9/2)² = 81/4π

Multiplying this by 1/9,
81/4π(1/9) = 81/36π = 9/4π