Gravel is being dumped from a conveyor belt at a rate of 50 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 17 feet high?Recall that the volume of a right circular cone with height h and radius of the base r is given byV=13πr2h
__ft/min
r = h/2.
v = 1/3 * π * r^2 * h ... substituting ... v = π/3 * h^3 / 4
differentiating with respect to time ... dv/dt = π/4 h^2 dh/dt
solve for dh/dt