The area of the shaded region of circle O is 9π m2

, and the measure of angle AOB

is 22.5 degrees. What is the length of the radius of circle O?

For full circle area is π * R² [here R = radius],

for a sector of circle with angle β, area will be = (β/2) * R², β is in radian,

here let β = 22.5° = (π * 22.5/180) = π/8 radian,

now [ (π/8) / 2] * R² = 9π, [π/16] * R² = 9π

R² = 9 * 16 = 144,

R = √144 = 12 m