Posted by crystal on .
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?

calc 
drwls,
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