What is the radius of a circle with a central angle of 4π7 radians that intercepts an arc of length 12π inches?

The answer is 21 in.

We have

Arc Length = r * theta (in rads) ....so......

12pi = r * (4/7 pi) divide out "pi"

12 = r ( 4/7) multiply both sides by 7/4

12 (7/4) = r = 84/4 = 21 inches