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)

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)

campbell_st · Answer

so in the area formula replace r with 2t

so 

$$A(r(t)) = \pi (2t)^2$$

then simplify it

part b substitute t = 5 and calculate the area

haseeb96 · Answer

it is very easy 
put r(t) =2t in area formula
A(r(t)) = pi*r^2
   = 3.14 x (2t)^2
    now solve it yourself and get your answer

haseeb96 · Answer

for Part B: you will put t=5 in the answer of Part A

anonymous · Answer

so just to make sure the final answer for part a 12.56t^2

haseeb96 · Answer

yes it is for Part A

haseeb96 · Answer

for part B as i said above you will just put t=5 at the place of t^2 in Part A's answer

anonymous · Answer

it would end up being 12.56(5)^2  @Haseeb96