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)

Please help me i'm stuck :(

Answer 1

Answer:

Part A:

Setting up the problem: A[r(t)] =  π (4t)^2

= Multiplying: A[r(t)] = 3.14 x 16t^2  

= Solving/Answer:  A[r(t)] = 50.24t^2

Part B: Area after 4 min of spilling = t=4

= r (4)= 4x4 =16

= Setting up the problem: A(16) = 3.14 x 16^2

= Multiplying:  A(16)= 3.14 x 256

= Solving/Answer: A(16) = 803.84

= The spilled area of milk after 4 min is 803.84.