Question

Find the area of the shaded sector. Leave your answer in terms of π.

Answer 1

Answer:

27π ft2

Step-by-step explanation:

We are given a circle with radius 9 feet and a shaded region with an angle of 120 degrees and we are to find the area of this shaded region.

Firstly, we will find the area of the whole circle and then multiply it with the ratio of the shaded region to the whole circle.

Area of the circle = $\pi r^2 = \pi (9)^2 = 81\pi$

Area of the shaded region = $\frac{120}{360} *81\pi =$ 27π ft2

Answer 2

Answer: Last option

Step-by-step explanation:

1. To solve this problem you must apply the following formula:

$A=\frac{x}{360}r^{2}\pi$

Where r is the radius and x is the measure of the central angle.

2. Keeping this on mind, you must substitute values, as you can see below. Then, you obtain the the area of the shaded region is:

$A=\frac{120}{360}(9ft)^{2}\pi$

$A=27\pi$ ft²