Answer:
201.45 cm²
Step-by-step 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:
[tex]81\pi\cdot\frac{57}{72}=9\pi\cdot\frac{57}{8}[/tex]
Using π ≈ 3.14 and crunching the numbers out gives us a result of approximately 201.45 cm².
