Question

Circle Y is shown. Line segments X Y and Z Y are radii. The length of X Y is 16. Sector X Y Z of the minor angle is shaded.

The measure of central angle XYZ is StartFraction 3 pi Over 4 EndFraction radians.

What is the area of the shaded sector?

32Pi units squared
85
96Pi units squared
256Pi units squared

Answer 1

96pi units²

Explanation:

Answer 2

½ × 16² × (3pi/4)

96pi units²

Explanation:

We can solve for the area of the sector using the formula [ A = 1/2 * r² * θ]. Note that θ equals the measure for the central angle which 3π/4

A = 1/2 * 16² * 3π/4

A = 1/2 * 256 * 3π/4

A = 128 * 3π/4

A = 3π128/4

A = 384π/4

A = 96π