Question

At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 2 cubic feet per minute. The diameter of the base of the cone is approximately three times the altitude. At what rate is the height of the pile changing when the pile is 2 feet high? (Hint: The formula for the volume of a cone is

V =
1
3
r2h.)

Answer 1

Using implicit differentiation, it is found that the height of the pile is changing at a rate of 0.1415 feet per minute when the pile is 2 feet high.

The height of the pile is changing at a rate of 0.1415 feet per minute when the pile is 2 feet high.