Question

Find the area of the shaded sector of the circle.

Answer 1

`192\pi \text{ ft}^2`

Explanation:

We can see that the shaded section of the circle is 3/4 of the total circle. This can be checked by comparing the angles measure of the shaded section with the angle of the entire circle:

`((360-90)\°)/(360\°)`

`=(270)/(360)`

`=(3)/(4)`

We can find its area by multiplying 3/4 by the area of the entire circle.

`A = (3)/(4) \cdot \pi r^2`

`A=(3)/(4) \cdot \pi \cdot 16^2`

`A = (3)/(4) \cdot \pi \cdot 256`

`\boxed{A = 192\pi \text{ ft}^2}`