Gravel is being dumped from a conveyor belt at a rate of 30 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always the same. How fast is the height of the pile increasing when the pile is 18 feet high?

Answer 1

dV/dt = d/dt[(pi/3)*R^2*H]
= 30 ft^3/min
= (pi/3)(1/4)*d/dt[H^3] since H= 2R

dV/dt = 30 = (pi/4)*3H^2*dH/dt

Solve for dH/dt when H = 18