Q:

A barrel of tomato sauce has spilled on a tile floor. The sauce flow can be expressed with the function r(t) = 2t, where t represents time in minutes and r represents how far the sauce is spreading.The spilled sauce is creating a circular pattern on the tile. The area of the pattern can be expressed as A(r) = πr2.Part A: Find the area of the circle of spilled sauce as a function of time, or A[r(t)]. Show your work. (6 points)Part B: How large is the area of spilled sauce after 5 minutes? You may use 3.14 to approximate π in this problem. (4 points)

Accepted Solution

A:
Part A: A[r(t)] = π(2t)^2 = 4πt^2

Part B: A(5) = 4 * 3.14 * 5^2 = 314