4 cubic feet per minute. The diameter of the base of the cone is approximately three times the altitude. At what rate (in ft/min) is the height of the pile changing when the pile is 22 feet high?

Answer 1

dV/dt = 4 ft/min

V=πr²h/3=πd²h/12=π9h³/12=3πh³/4

dV/dt = 9πh²/4 dh/dt

dh/dt = (4/(9πh²))dV/dt)

when dV/dt =4 and h=22

dh/dt = 16/(4356π) ft/min