Question

Find the area of the blue sector. Use 3.14 for pi and round to the nearest hundredth.

A)
0.52 in2

B)
3.66 in2

C)
25.64 in2

D)
128.22 in2

*I would like to know how you did it too, it would really help me*

Answer 1

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

notice your picture, you have both, so, just plug them in

Answer 2

Option C
`25.64\ in^(2)`

Explanation:

we know that

The area of a circle is equal to

`A=\pi r^(2)`

we have

`r=7\ in`

substitute

`A=\pi(7)^(2)=49\pi\ in^(2)`

Remember that

`360` degrees subtends the complete area of the circle

so

by proportion

Find the area of the blue sector for an angle of
`60` degrees

`(49\pi)/(360)=(x)/(60)\\ \\x={49\pi*60/360`

`x=25.64\ in^(2)`