Find exact radius of circle please help!

Explanation:

Let r be the radius we want to find

The area of the full circle is A = pi*r^2

The unshaded portion is 60 degrees, so the unshaded portion must be 360-60 = 300 degrees.

The full area was pi*r^2, but we only want 300/360 of that full area.

So,

s = shaded area

s = (300/360)*(full circle area)

s = (300/360)*(pi*r^2)

s = 30pi

(300/360)*(pi*r^2) = 30pi

(300/360)*r^2 = 30

(5/6)*r^2 = 30

5r^2 = 30*6

5r^2 = 180

r^2 = 36

r = sqrt(36)

r = 6

The radius is 6 inches.