Question

Please help ! :)

Liza is creating a circular mirror using pie-shaped pieces of glass, as shown below. How much wall space will the entire mirror cover? Use 3.14 for Pi and round to the nearest whole number.

Answer 1

Answer: Third option.

Explanation:

You know that:

`(Area\ of\ sector)/(Area\ of\ circle)=(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:

`(A_s)/(A_c)=(n)/(360\°)`

Now, you need to solve for
`A_c`:

`A_s=((n)/(360\°))(A_c)\\\\A_c=(A_s)((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)((360\°)/(40\°))\\\\A_c=169.56\ in^2\\\\A_c\approx170\ in^2`

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