The logo for a new company is a circle divided into 24 equally sized sectors. Six of the sectors are white, and the others are different colors.
The area of one of the white sectors is 13π50 inches squared.
What is the radius of the circle?
The angluar measure of each of the sectors = 360/24 = 15° = 15/180 pi = pi/12 rads
The area,A, of a sector with a central angle measure in rads (theta) is given by
A =(1/2)* r^2 *(theta)
13pi/50 = (1/2) *r^2* ( pi/12)
13/50 = r^2 / 24
24*13 / 50 = r^2
312/50 = r^2
sqrt (312/50) = r ≈ 2.5 in