The area of the shaded region of circle \(O\) is \(9\pi \, \text{m}^2\), 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

Answered by here2help | 2024-06-10