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) =
which is
V(h) =
or
V(h) =
:
let t = time in minutes, h = 3 inches to start with, therefore the height:
(3+.5t)
V(t) =
:
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
= 70
Multiply both sides by
(reciprocal gets rid of
on the left)
3 + .5t = 70 *
:
3 + .5t =
3 + .5t = 89.126
.5t = 89.126 - 3
.5t = 86.126
t =
t = 172.25 min to reach 70 cu/inches
;
:
Check this in the volume equation: t=172.25
V(t) =
V(t) =
V(t) =
V(t) = 69.9986 ~ 70
;
:
Two hrs is a long time, hope this has helped!
