Question

Circle R is shown. Line segments Q R and S R are radii. The length of Q R is 18. Sector Q R S is shaded.
The measure of central angle QRS is StartFraction 8 pi Over 9 EndFraction radians.

What is the area of the shaded sector?

36Pi units squared
72Pi units squared
144Pi units squared
324Pi units squared

Answer 1

Area of a sector = (1/2) r^2 θ. Here r = 18 and θ = 8π/9, so

Area = (1/2)(18^2)(8π/9) = (1/2)(324)(8π/9) = 162*(8π/9) = 144π.

Answer: 144Pi units squared.