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

R(t) = 4t
A(r) = π(r^2)

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

b) t = 4,

A(4) = 16*3.14*(16)^2 = 12,861.44