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) = πr^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

@pooja195 @ganeshie8

Answer 2

@KendrickLamar2014

Answer 3

@Mehek14 @mayankdevnani

Answer 4

@mayankdevnani @pooja195

Answer 5

For part A you plug in r(t) in A(r)
A[r(t)] = π(4t)^2 = 16 π t^2
For part B you plug in 4 in A[r(t)]
A[r(4)] = 16 π t^2 = 16 * 3.14 * 4^2 = ...

Answer 6

Part A;
\[r=4t\]
\[a=\pi r ^{2}\]
\[a=\pi (4t)^2\]
\[a=16 \pi t^2\]

Part B:
\[a=16 \pi (4)^2\]
= 803.84 units