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 (-10, 2) 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

Bob will need approximately 530.929 square feet of tile for the circular floor of his restaurant. This is calculated using the distance formula to determine the radius of the circle, and then using the area formula for a circle, A = πr^2.

Step-by-step explanation:

To calculate the number of square feet of tile needed for Bob's Burgers' circular floor, we first need to find the diameter of the circle which represents the floor. The distance between the front door at (-10, 2) and the center of the restaurant at (2, -3) forms the radius of the circle. We can find this distance using the distance formula sqrt((x2-x1)^2 + (y2-y1)^2). Thus, the radius is sqrt((2 - (-10))^2 + (-3 - 2)^2) = sqrt((12)^2 + (-5)^2) = sqrt(144 + 25) = sqrt(169) = 13 feet. To find the area, we use the formula A = πr^2, where A is the area, π is the constant pi (approximately 3.14159), and r is the radius.

The area of the circular floor is A = π * (13 feet)^2 = 3.14159 * 169 = approximately 530.929 square feet. Therefore, Bob will need approximately 530.929 square feet of tile for his restaurant.