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 14 feet high?

Question

Recall that the volume of a right circular cone with height h and radius of the base r is given byV=13πr2h

Answer: ____Ft/ Min

Answer 1

V = (1/3) pi r^2 h I think you mean
h = 2 r given
V = (2/3) pi r^3
dV/dt = (2 pi/3) 3 r^2 dr/dt = 2 pi r^2 dr/dt
10 = 2 pi (14)^2 dr/dt
solve for dr/dt
dh /dt = 2 dr/dt

Answer 2

I'm confused