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 equal. How fast is the height of the pile increasing when the pile is 13 feet high. Recall that the volume of a right circular cone with the height h and radius of the base r is given by

V=1/3pi r*2h

Answer in ft/min

Answer 1

let assume that the base diameter of cone is d and height is h,

the volume of the cone,

put dV/dt = 10, h = 13,