Question

Find the area of the shaded part of circle Y.

Answer 1

201.45 cm²

Explanation:

The whole circle has an area of π(9)² cm², or 81π cm². The shaded part represents all of the circle except for the chunk swept out by sector XZ.

Sector XZ sweeps out 75°, which represents 75/360 of the whole circle, or, simplified, 15/72. That means the shaded area must represent the other 57/72. To find the area then, we can just multiply that fraction by 81π:

`81\pi\cdot(57)/(72)=9\pi\cdot(57)/(8)`

Using π ≈ 3.14 and crunching the numbers out gives us a result of approximately 201.45 cm².