Question

A vat of milk has spilled on a tile floor. The milk flow can be expressed with the function r(t) = 4t, where t represents time in minutes and r represents how far the milk is spreading.

The spilled milk 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 milk as a function of time, or A[r(t)]. Show your work. (6 points)

Part B: How large is the area of spilled milk after 4 minutes? You may use 3.14 to approximate π in this problem. (4 points)

Answer 1

Part A

Area = π[r(t)^]2 = π[(4t)^2] =16π(t)^2

Part B

t = 4 min

Area = 16(3.14)(4)^2= 803.84