Related Rates and changes

Question

Sand is falling off a conveyor belt and onto a conical pile at a rate of 12 cubic feet per minute. The diameter of the base of the cone is approximately 4 times the height of the pile. A) At what rate is the height of the pile changing when the pile is 10 feet high? B) At what rate is the area of the base fo the pile changing when the pile is 10 feet high?

Answer 1

The volume of a cone is (1/3)πr²h.

In this problem r=2h or h=(1/2)r

Hence V = (1/6)πr³

dV/dt = (1/2)πr² dr/dt

With this information you should now be able to answer the question. Remember the relation between r and h!