Water is leaking out of an inverted conical tank at a rate of 60000 cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has height 90 meters and the diameter at the top is 40 meters. If the water level is rising at a rate of 300 centimeters per minute when the height of the water is 30 meters, find the rate at which water is being pumped into the tank in cubic centimeters per minute.

Answer 1

The key is writing volume as function of height of water.
Volumecone= 1/3 h*basearea=1/2*h(20/90)^2PI
take the derivative, dh/dt= 3m/min, find dV/dt