Water is leaking out of an inverted conical tank

Question

Water is leaking out of an inverted conical tank at a rate of 8700 cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has height 6 meters and the diameter at the top is 4.5 meters. If the water level is rising at a rate of 28 centimeters per minute when the height of the water is 5 meters, find the rate at which water is being pumped into the tank in cubic centimeters per minute.

Answer 1

This is just a complicated related rate problem.

You need to know 3 things:

1> V=(1/3)πr²h

2>r/h=2.25/6

3>dV/dt=F-8700 where F is the flow rate you want

From 1 and 2 you can derive a formula for dV/dt in terms of dh/dt which is given.

Set the 2 expressions for dV/dt equal to each other and solve for F.

Complicated and messy but NOT difficult!