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) = π r^2. part a: find the area of the circle of spilled milk as a function of time, or a[r(t)]. part b: how large is the area of spilled milk after 4 minutes? you may use 3.14 to approximate π in this problem.

Answer 1

4t=r
a=pir^2
sub 4t for r
a=pi(4t)^2
a=pi16t^2
a(t)=16pi(t^2)


A. a(t)=16pi(t^2)

B. sub 4 for t
a(4)=16pi4^2
a(4)=16pi16
a(4)=16*16*3.14
a(4)=803.84 square units



A. a(t)=16pi(t^2)
B. 803.84 square units

Answer 2

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.