Question

central angle of a sector is 72° and the sector has an area of 16.2(pie) ft^2. what is the radius of the circle?

Answer 1

Sector area = (central angle / 360) * PI * radius^2
sector area = (72 / 360) * PI * radius^2
radius^2 = sector area / [(72 / 360) * PI]
radius^2 = 16.2 * PI / [(1 / 5) * PI]
radius^2 = 16.2 / .2
radius^2 = 81
radius = 9

Source:
http://www.1728.org/radians.htm