Question

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

Answer 1

Radian measure is given by dividing the length of an arc by the radius of a given circle. Such that an arc that subtends an angle of 1 radian to the center of a circle is equivalent to the radius of the circle. 
Therefore; θ = s/r where θ is the angle subtended in radians, s is the length of the arc and r is the radius of the circle.
Hence; r = s/θ
               =  12π ÷ (4π/7)
               = 12 × (7/4)
               = 21 inches