Question

Please help ! :)

Answer 1

Answer: Third option.

Step-by-step explanation:

You know that:

$\frac{Area\ of\ sector}{Area\ of\ circle}=\frac{n}{360\°}$

Where "n" is the Central angle measured in degrees.

In this case, let be:

$Area\ of\ sector=A_s\\Area\ of\ Circle=A_c$

Rewriting the formula:

$\frac{A_s}{A_c}=\frac{n}{360\°}$

Now, you need to solve for $A_c$:

$A_s=(\frac{n}{360\°})(A_c)\\\\A_c=(A_s)(\frac{360\°}{n})$

Given the data shown in the picture attached, you can identify that:

$A=A_s=6\pi \ in^2\\\\n=40\°$

Then, you can substitute these values into the equation (Use $\pi =3.14$):

$A_c=(6*3.14\ in^2)(\frac{360\°}{40\°})\\\\A_c=169.56\ in^2\\\\A_c\approx170\ in^2$

Therefore, the entire mirror will cover $170\ in^2$