Question

Water is leaking out of an inverted conical tank at a rate of 11300.0 cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has height 10.0 meters and the diameter at the top is 7.0 meters. If the water level is rising at a rate of 19.0 centimeters per minute when the height of the water is 4.5 meters, find the rate at which water is being pumped into the tank in cubic centimeters per minute. How the hell do you sove this?

Answer 1

\[
\text{From similar triangles:} \\
\frac rh = \frac {3.5}{10} = 0.35 \\
r = 0.35h \\
V = \frac 13 \pi r^2h = \frac 13 \pi (0.35h)^2h = 0.12828h^3 \\
\frac {dV}{dt} = 0.12828(3h^2)\frac{dh}{dt} = 0.3848h^2\frac{dh}{dt} \\
\frac {dV}{dt} = \text{rate of volume in - rate of volume out} = \\
(x - 11300)*10^{-6} ~m^3/min = 0.3848h^2\frac{dh}{dt} \\
\text{Plug in the values and solve for x.} \\
h = 4.5~m; ~~~~dh/dt = 19~ cm. / min = 0.19~ m /min.
\]

Answer 2

That is not the answer

Answer 3

This is so hard....

Answer 4

Someone please help!

Answer 5

http://openstudy.com/study#/updates/4f5acdb0e4b0602be437a3e3 try this it might help :)

Answer 6

its not the same numbers but it might help ya

Answer 7

It was asking it in centimeters per minute woops lol

Answer 8

Got it guys thanks! I forgot it was asking for it in centimeters per minute not meters per minute. The answer was 1491991.522