Question

A barrel of tomato sauce has spilled on a tile floor. The sauce flow can be expressed with the function r(t) = 2t, where t represents time in minutes and r represents how far the sauce is spreading.

The spilled sauce 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 sauce as a function of time, or A[r(t)]. Show your work. (6 points)

Part B: How large is the area of spilled sauce after 5 minutes? You may use 3.14 to approximate π in this problem. (4 points)

Answer 1

Part A:
Given in the statement
r(t)= 2t
A(r) = πr2
So to find A[r(t)]
You have to plug r(t) into A(r)
Answer: A[r(t)] =π(2t)2=4πt

Part B:
The statement tells you t=5 min and
π=3.14

So plug in you values
A[r(t)]=π(2(5))2=4* 3.14*5=62.8