Question

Water is flowing at the rate of 50 m^3/min from a conical reservoir (vertex down) of base radius 45 meters and height 6 meters. What is the water level when the reservoir has 5000 m^3 of water left in it?

Answer 1

Since the ratio of radius/height is constant at any water depth (45/6 when full), r = 15/2 h. You want h when v=5000.

v = 1/3 πr^2 h, so
π/3 (15/2 h)^2 h = 5000
π/3 * 225/4 h^3 = 5000
h^3 = 12*5000/225 = 800/3
h = 6.43m