Answer: Radius = 6 inches
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Step-by-step 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.