Problem 1181

Find the area of a sector of a circle having radius r and central angle θ.

r = 70.0 mi, θ = 100°

Solution:-

First , multiply the degree measure of the angle by $\frac{\pi}{180}$ and simplify to convert to radians.

100°( $\frac{\pi}{180}$ ) = $\frac{5\pi}{9}$ radian

The area A of a sector of a circle of radius r and central angle θ (in radians) is given by the following formula.

A = $\frac{1}{2}$ r²θ,θ in radians

Substitute the values r = 70.0 and θ = $\frac{5\pi}{9}$ radian into the formula shown above and simplify.

A = $\frac{1}{2}$ (70.0)² ( $\frac{\5pi}{9}$ ) $\approx$ 4276.1 mi²

Therefore, the area of the sector is approximately 4276.1 mi².