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

b. 19.54 ft²

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=(1)/(2)r^(2) \theta`

Where the angle
`\theta` is in radians.

35 degrees in radian would be =
`35 * (\pi)/(180) = (7 \pi)/(36)`

Using the values in the formula, we get:

`Area = (1)/(2) * (8)^(2) * ((7 \pi)/(36) )\\\\ Area = 19.54`

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