Gravel is being dumped from a conveyor belt at a rate of 30ft^3/min and its coarseness is such that it forms a

Question

pile in the shape of a cone whose base diameter and height are always equal.How fast is the height of the pile increasing when the pile is 10 ft high?

Answer 1

The volume V of a cone is given by

V = (1/3)π r² h

where r is the base radius and h is the height.

We're told that the base diameter always equals the height, so the base radius is always half of the height. Putting that in the volume formula,

V = (1/3)π (h/2)² h = (1/12)π h³

We know what dV/dt is. Find dh/dt when h=10.