An inverted conical tank (with vertex down) is 14 feet across the top and 24 feet deep. if water is flowing in at a rate of 12 ft3/min, find the rate of change of the depth of the water when the water is 10 feet deep.
Let dV = dt = water is flowing in at a rate of 12 ft3 / min. h = the depth of the water. dh / dt = the rate of change of the depth. First you must find the volume of the cone as a function of "h". Then you must derive the volume of the cone with respect to time. Finally clear dh / dt. I attach the solution.
