Question

Water is leaking out of an inverted conical tank at a rate of 11600 cubic centimeters per minute at the same time that water is being pumped into the tank at a constant rate. The tank has height 7 meters and the diameter at the top is 7 meters. If the water level is rising at a rate of 18 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.

Answer 1

V= pi/3 r^2 *h = pi/3(h/2)^2 *h

Answer 2

differentiate with respect to time
plug in h and dh/dt
find dV/dt
amount pumped in - amount leaking out = dV/dt