At what rate (in ft/min) is the height of the pile changing when the pile is 12 feet high?

Question

At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 2 cubic feet per minute. The diameter of the base of the cone is approximately three times the altitude.

Answer 1

Let b = the diameter of the base of the pile and h = the ht of the pile; b = 3h

Volume V = (1/3)π(b/2)²h = 3πh³/4

dv/dt = (9πh²/4) dh/dt

Now just plug in the values given to get you answer.