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scoray [572]
3 years ago
5

Please help ! :)

Mathematics
1 answer:
kolezko [41]3 years ago
8 0

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

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