Question

What is the area of the sector bound by the center of the circle and arc CD in the circle below?

Circle A is shown with a radius labeled 8 feet and a central angle marked 35 degrees.

a
9.42 ft2

b
19.54 ft2

c
34.89 ft2

d
88.31 ft2

Answer 1

Answer:

b. 19.54 ft²

Step-by-step explanation:

Measure of the central angle made by the arc CD = 35 degrees

Measure of radius of circle = r = 8 feet

Area of the sector is calculated as:

$A=\frac{1}{2}r^{2} \theta$

Where the angle $\theta$ is in radians.

35 degrees in radian would be = $35 \times \frac{\pi}{180} = \frac{7 \pi}{36}$

Using the values in the formula, we get:

$Area = \frac{1}{2} \times (8)^{2} \times (\frac{7 \pi}{36} )\\\\ Area = 19.54$

Thus, the area of the sector bounded by arc CD would be 19.54 ft²