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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

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 an class=

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musiclover10045
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.


isyllus

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:

[tex]\text{Area of sector}=\dfrac{\theta}{360}\times \pi r^2[/tex]

where,

[tex]\theta = 40^\circ[/tex]

[tex]r=10\ ft[/tex]

Substitute the value into formula

[tex]\text{Area of sector}=\dfrac{40}{360}\times \pi \cdot 10^2[/tex]

[tex]\text{Area of sector}=\dfrac{100\pi}{9}[/tex]

[tex]\text{Area of sector}=34.89\text{ ft}^2[/tex]

Hence, The area of sector is 34.89 ft²

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