SOLUTION: A cylindrical container has 3 inches of water in it and is being filled at a rate of 1/2 inch per minute. The volume, V, of the water in the container is given by the function: V(h

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Question 241152: A cylindrical container has 3 inches of water in it and is being filled at a rate of 1/2 inch per minute. The volume, V, of the water in the container is given by the function: V(h)=(π/4)h^3. Write a formula for the volume in terms of the time in minutes. Then, calculate the ammount of time that will take to fill the container to 70 cubic inches.
please.....help!!!!! i have been working from 2 hours!!!!!
and also (π = pi)mathematic pi.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A cylindrical container has 3 inches of water in it and is being filled at a rate of 1/2 inch per minute.
The volume, V, of the water in the container is given by the function: V(h)=(π/4)h^3.
Write a formula for the volume in terms of the time in minutes.
:
The formula appears to be the volume of a cylinder with a radius of 1/2 inch
V(h) = pi%2A%281%2F2%29%5E2+%2A+h
which is
V(h) = pi%2A%281%2F4%29+%2A+h
or
V(h) = %28pi%2F4%29%2Ah
:
let t = time in minutes, h = 3 inches to start with, therefore the height:
(3+.5t)
V(t) = %28pi%2F4%29%2A%283%2B.5t%29
:
Then, calculate the amount of time that will take to fill the container to 70 cubic inches.
Replace V(t) with 70, solve for t
%28pi%2F4%29%2A%283%2B.5t%29 = 70
Multiply both sides by 4%2Fpi (reciprocal gets rid of %28pi%2F4%29 on the left)
3 + .5t = 70 * 4%2Fpi
:
3 + .5t = 280%2Fpi
3 + .5t = 89.126
.5t = 89.126 - 3
.5t = 86.126
t = 86.126%2F.5
t = 172.25 min to reach 70 cu/inches
;
:
Check this in the volume equation: t=172.25
V(t) = %28pi%2F4%29%2A%283%2B.5t%29
V(t) = %28pi%2F4%29%2A%283%2B.5%28172.25%29%29
V(t) = %28pi%2F4%29%2A89.125
V(t) = 69.9986 ~ 70
;
:
Two hrs is a long time, hope this has helped!