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.

Answer 1

Part A: Find the area of the circle of spilled milk as a function of time, or A[r(t)].
A(r(t)) = A(4t) = π(4t)^2 = 16πt^2
A[r(t)] = 16πt^2

Part B: How large is the area of spilled milk after 4 minutes? You may use 3.14 to approximate π in this problem.
After 4 minutes, A = 16(3.14)(4)^2 = 803.84 cubic meters.