Question

The measure of central angle XYZ is 1.25 radians.

Circle Y is shown. Line segments X Y and Z Y are radii. The length of X Y is 8. The major angle of X Y Z is shaded.

What is the area of the shaded sector?

10 units2
20 units2
40 units2
80 units2

Answer 1

Area of a sector (θ in radians) = (1/2) r^2 θ. Here r = 8 and θ = 1.25, so

Area = (1/2)(8^2)(1.25) = 32 · 1.25 = 40 units^2.

(If the major sector were shaded its area would be 64π − 40 ≈ 161.06, not one of the choices.)