Question

related rates calculus question, please help!

Answer 1

Water is leaking out of an inverted conical tank at a rate of 29000 cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has height 120 meters and the diameter at the top is 65 meters. If the water level is rising at a rate of 280 centimeters per minute when the height of the water is 40 meters, find the rate at which water is being pumped into the tank in cubic centimeters per minute.

Answer 2

They also give a hint: Note: Let "R" be the unknown rate at which water is being pumped in. Then you know that if V is volume of water, \[\frac{ dV }{ dt }\]=R−29000. Use geometry (similar triangles?) to find the relationship between the height of the water and the volume of the water at any given time. Recall that the volume of a cone with base radius r and height h is given by \[\frac{ 1 }{ 3 }pir ^{2}h\].