Question

Bob is building a new restaurant called Bob's Burgers. He wants the building to be shaped like a burger, and he needs to figure out how many square feet of tile he will need for the circular floor inside of the restaurant. The blueprints for the building are graphed with the front door located at (-1, 5) and the center of the restaurant located at (2, -3) where each unit on the grid is 1 foot. How many square feet of tile will Bob need for the floor of Bob's Burgers?

Answer 1

To calculate the area needed for tiling the floor of Bob's Burgers, determine the distance between the front door and center of the restaurant to find the radius, then use the area formula for a circle. Bob will need approximately 229.22 square feet of tile.

Step-by-step explanation:

The task here is to calculate the area of the circular floor inside Bob's Burgers restaurant. To find this, we need to determine the radius of the circle, which can be done by calculating the distance between the front door at (-1, 5) and the center at (2, -3). By using the distance formula \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\), we get \(d = \sqrt{(2 - (-1))^2 + (-3 - 5)^2} = \sqrt{3^2 + (-8)^2} = \sqrt{9 + 64} = \sqrt{73}\) feet. Hence, the radius of the circle is \(\sqrt{73}\) feet. The area of a circle is found with the formula \(A = \pi r^2\), which gives us \(A = \pi (\sqrt{73})^2 = 73\pi\) square feet. Therefore, Bob will need 73\pi square feet of tile, approximately 229.22 square feet (using 3.14 for \(\pi\)) for the circular floor of his restaurant.