Question

A conical tank 20 feet in diameter and 30 feet tall is leaking water at a rate of 5pi cubic feet per hour. At what rate is the water level dropping when the water is 15 feet deep? (Show a complete solotion) PLEASE HELP~!!!!!

Answer 1

By symmetry, at 15 feet depth, the diameter of the water surface in the tank = 10 ft.
Volume of water in cone = (1/3)(pi)(5^2)(15)
After 1 hr (assuming the same rate of leakage),
Vol of water remaining = 125pi - 5pi = 120pi ft^3
120 = (1/3)(pi)(25m^2)(15m) (where m is the ratio of the new depth to 15ft)
m = cbrt(0.96/pi) = 0.673556; 1-m = 0.326444
Hence the rate of fall of the water level when the depth of water in the cone is 15 ft = (0.326444 * 15) ft/h = 4.8967 ft/h (Answer)
(take note that I have used the full decimal representation instead of the rounded value for this working)

Answer 2

Thank you~