Question

Gravel is being dumped from a conveyor belt at a rate of 10 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 11 feet high? Recall that the volume of a right circular cone with height h and radius of the base r is given by V= (1/3)pi r^2h

Answer 1

Given that \(r=h\), the volume would be
\[V=\frac{1}{3}\pi h^3\]
Differentiating, you have
\[\frac{dV}{dt}=\pi h^2\frac{dh}{dt}\]
with \(h=11\) and \(\dfrac{dV}{dt}=10\).