#### Answer

8 in

#### Work Step by Step

Given the length of the arc is 4$\pi$ in which is 90$^{\circ}$ arc
We need to find out the length of the radius of the circle
In a circle whose circumference is c, the length l of an arc whose degree measure is m is given by l =$\frac{m}{360}$ * c
where c = 2$\pi$ r , m= 90$^{\circ}$
l= 4$\pi$ in.
Therefore 4$\pi$ = $\frac{90}{360}$ * 2$\pi$ r
r = 4*2 = 8 in.
The radius of the circle = 8 in