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.

 

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