Andy wants to order a cookie cake for a birthday party. He plans to split between 12 people, with each person getting a piece that is at least 4 square inches. What is the radius of the smallest size cookie cake he could get?
So he wants the area to be 4(12) or 48 inches^2
πr^2 = 48
r^2 = 48/π
r = appr 3.9 inches
To find the radius of the smallest size cookie cake that Andy could get, we need to determine the area of each piece of cake.
First, we need to calculate the total area of the cake that needs to be divided among the 12 people. We can calculate this by multiplying the area of each piece (4 square inches) by the number of people (12):
Total area = 4 square inches * 12 = 48 square inches
Since the cookie cake is circular, the area of the cake can be determined using the formula for the area of a circle: A = πr^2, where A is the area and r is the radius.
Therefore, we need to solve the equation: πr^2 = 48 square inches.
To find the radius, we can rearrange the equation and isolate r:
r^2 = 48 square inches / π
r^2 ≈ 15.28 square inches (using the approximate value of π ≈ 3.14)
Taking the square root of both sides, we find:
r ≈ √15.28 inches
Therefore, the radius of the smallest size cookie cake that Andy could get is approximately 3.91 inches.