Question

Find exact radius of the circle. Please help!

Answer 1

Answer:    Radius = 6*sqrt(3) meters

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Work Shown:

The unshaded portion is 310 degrees, while the shaded portion is 360-310 = 50 degrees

This means 50/360 = 5/36 of the full circle area is the shaded region of 15pi square meters

So,

s = shaded area = 15pi

s = (5/36)*(full circle area)

s = (5/36)*(pi*r^2)

(5/36)*(pi*r^2) = 15pi

(5/36)*r^2 = 15

5r^2 = 15*36

5r^2 = 540

r^2 = 540/5

r^2 = 108

r = sqrt(108)

r = sqrt(36*3)

r = sqrt(36)*sqrt(3)

r = 6*sqrt(3)