Question

Help with related rates?
Water is leaking out of an inverted conical tank at a rate of 6400.0 cubic centimeters per minute at the same time that water is being pumped into the tank at a constant rate. The tank has a height of 7.0 meters and the diameter at the top is 4.0 meters. If the water level is rising at a rate of 21.0 centimeters per minute when the height of the water is 2.5 meters, find the rate at which water is being pumped into the tank in cubic centimeters per minute.

Answer 1

Ok let's try to set this up properly, maybe we can get an idea of what's going on..

Answer 2

When the height is 250cm, the rate of change of the height, \(\large \dfrac{dh}{dt}=21\text{cm}\)

Answer 3

Grr these cone problems always confuse me -_- hmmm let's see..

Answer 4

They also gave us the rate of change of the Volume, \(\Large \dfrac{dV}{dt}=-6400\)

Answer 5

Err woops I messed that up.
That's the rate at which liquid is flowing out.

\[\Large \frac{dV}{dt}=\text{rate in}+\text{rate out}\]

Answer 6

Okay, I got that

Answer 7

hmmmm

Answer 8

I'm guessing I have to find r, plug that in to the volume and then differentiate

Answer 9

ya it's probably this thing with similar triangles.\[\Large \frac{r}{250}=\frac{200}{700}\]