Question

Question 1 (1 point) v SurvedSheila is building a new restaurant called Sheila's Scoops. She wants the building tobe shaped like a scoop of ice cream, and she needs to figure out how many squarefeet of tile she will need for the circular floor inside of the restaurant. The blueprintsfor the building are graphed with the front door located at (-6, 2) and the center ofthe restaurant located at (6,-3) where each unit on the grid is 1 foot. How manysquare feet of tile will Sheila need for the floor of Sheila's Scoops? Show your workand explain each step you take to solve using proper math vocabulary.

Answer 1

Let's find the equation of the circle using the general equation for the circle:

`(x-h)^2+(y-k)^2=r^2`

where ( h, k ) is the center and r is the radius.

we know the center which is (6,-3), so:

`\begin{gathered} (x-6)^2+(y-(-3))^2=r^2 \\ (x-6)^2+(y+3)^2=r^2 \end{gathered}`

Also, we know one of the points of the circle, so:

`\begin{gathered} (-6,2) \\ (-6-6)^2+(2+3)^2=r^2 \\ (-12)^2+(5)^2=r^2 \\ 144+25=r^2 \\ so\colon \\ r^2=169 \\ r=\sqrt[]{169} \\ r=13 \end{gathered}`

Since we know the radius of the circle, we can find the area easily with the following formula:

`\begin{gathered} A=\pi r^2 \\ A=\pi(13)^2 \\ A=169\pi ft^2^{} \\ A\approx530.93ft^2 \end{gathered}`