Find the rate at which water is being pumped into the tank

Question

Water is leaking out of an inverted conical tank at a rate of 11,000 cm³/min at the same time that water is being pumped into the tank at a constant rate. The tank has height 6 m and the diameter at the top is 4 m. If the water level is rising at a rate of 20 cm/min when the height of the water is 2 m, find the rate at which water is being pumped into the tank. (Round your answer to the nearest integer.)

 cm³/min

Answer 1

Volume of water is V = 1/3πr²h; h/r = 6/2 = 3; r = h/3;

V = 1/3πh³/9 = πh³/27.

dV/dt = c - 11000, where c in cm³/min;

πh²/9·dh/dt = c - 11000; c = 11000 + π(200)²/9·20 = 290252.68 cm³/min