Gravel is being dumped from a conveyor belt at a rate of [math] 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 [math] feet high? Recall that the volume of a right circular cone with height [math] and radius of the base [math] is given by [math].

When the pile is [math] feet high, its height is increasing at feet per minute.

Solution: