Answer: Third option.
Step-by-step explanation:
You know that:
[tex]\frac{Area\ of\ sector}{Area\ of\ circle}=\frac{n}{360\°}[/tex]
Where "n" is the Central angle measured in degrees.
In this case, let be:
[tex]Area\ of\ sector=A_s\\Area\ of\ Circle=A_c[/tex]
Rewriting the formula:
[tex]\frac{A_s}{A_c}=\frac{n}{360\°}[/tex]
Now, you need to solve for [tex]A_c[/tex]:
[tex]A_s=(\frac{n}{360\°})(A_c)\\\\A_c=(A_s)(\frac{360\°}{n})[/tex]
Given the data shown in the picture attached, you can identify that:
[tex]A=A_s=6\pi \ in^2\\\\n=40\°[/tex]
Then, you can substitute these values into the equation (Use [tex]\pi =3.14[/tex]):
[tex]A_c=(6*3.14\ in^2)(\frac{360\°}{40\°})\\\\A_c=169.56\ in^2\\\\A_c\approx170\ in^2[/tex]
Therefore, the entire mirror will cover [tex]170\ in^2[/tex]
