Water is leaking out of an inverted conical tank at a rate of 9,500 cm^3/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.)

Answer 1

You know that when the water has depth y, the surface of the water has radius (4/6)y

So, at depth y, the volume of water is

v = π/3 r^2 y = π/3 (4/9) y^3
dv/dt = 4π/9 y^2 dy/dt

That's if no water is draining out. SO, adjust dv/dt when you get your answer above.