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

Answer:

Hence, The area of sector is 34.89 ft²

C is correct.

Step-by-step explanation:

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

Formula:

$\text{Area of sector}=\dfrac{\theta}{360}\times \pi r^2$

where,

$\theta = 40^\circ$

$r=10\ ft$

Substitute the value into formula

$\text{Area of sector}=\dfrac{40}{360}\times \pi \cdot 10^2$

$\text{Area of sector}=\dfrac{100\pi}{9}$

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

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.