A conical water tank with vertex down has a radius of 13 feet at the top and is 27 feet high. If water flows into the tank at a rate of 30 ft^3/min, how fast is the depth of the water increasing when the water is 17 feet deep?

Answer 1

v = 1/3 * π * r^2 * h

r = 13/27 h

v = 1/3 * π * (13/27 h)^2 * h = 1/3 * π * (13/27)^2 * h^3

dv/dt = π * (13/27)^2 * h^2 * dh/dt

30 ft^3/min = π * (13/27)^2 * (17 ft)^2 * dh/dt