Question

a conical tank is 15 feet deep and has an open top whose radius is 15 feet. Assume that starting at t = 0 water is added to the tank at a rate of pi ft^3/hr, and water evaporates from the tank at a rate proportional to the suface area with the constant of proportionality being 0.01. The tank is assumed to be empty at time t = 0. Let V and h represent the volume and depth of water in the tank.

solve the equation dh/dt = (1-0.01h^2)/h^2

Answer 1

Use separation of variables.

Integrate

dt = h^2/(1-0.01h^2) dh

with h = 0 at t = 0