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 10 feet and a central angle marked 40 degrees.

A) 9.42 ft2
B) 19.54 ft2
C) 34.89 ft2
D) 88.31 ft2

Answer 1

Hence, The area of sector is 34.89 ft²

C is correct.

Explanation:

Given: Circle A is shown with a radius labeled 10 feet and a central angle marked 40 degrees.

Formula:

`\text{Area of sector}=(\theta)/(360)* \pi r^2`

where,

`\theta = 40^\circ`

`r=10\ ft`

Substitute the value into formula

`\text{Area of sector}=(40)/(360)* \pi \cdot 10^2`

`\text{Area of sector}=(100\pi)/(9)`

`\text{Area of sector}=34.89\text{ ft}^2`

Hence, The area of sector is 34.89 ft²

Answer 2

The area of the full circle is PI x r^2
r = 10
r^2 = 100

Area = 100*3.14 = 314 square feet.


Area of sector:
314 * 40/360 = 34.89 square feet.
The answer is C.