Question

To the nearest square inch, what is the area of the shaded sector in the circle shown below?

A) 464 in2
B) 23 in2
C) 314 in2
D) 116 in2

Answer 1

`\bf \textit{area of a sector of a circle}\\\\ A=\cfrac{\theta r^2\pi }{360}\qquad \begin{cases} \theta =\textit{angle in degrees}\\ r=radius\\ ----------\\ r=10\\ \theta =133 \end{cases}\implies A=\cfrac{133\cdot 10^2\cdot \pi }{360}`

Answer 2

The answer is the option D

`116\ in^(2)`

Explanation:

we know that

The area of a circle is equal to

`A=\pi r^(2)`

where

r is the radius of the circle

In this problem we have

`r=10\ in`

Substitute

`A=\pi 10^(2)=100\pi\ in^(2)`

Remember that

`360\°` subtends the area of the complete circle

so

by proportion

Find the area of the shaded sector for an angle of
`133\°`

`(100\pi)/(360) (in^(2))/(degrees)=(x)/(133) (in^(2))/(degrees) \\ \\x=133*100\pi/360\\ \\x= 116\ in^(2)`