For a particular circle, a central angle of 75 degrees will intercept an arc of length 10pi feet. What is the radius of this circle?

lets find the total circumference. 10\pi*4.8= 48\pi

we know the circumference is 2pi*r

so 48pi/2pi=24

r=24

10pi =75 x pi/180 x r(radius), solve for r

10pi = 5/12 pi x r multiply both sides by 12/5 pi

r =12/5 pi x 10 pi

r = 24 - Radius of this circle.