At a sand and gravel plant, sand is falling off a conveyor belt and onto a conical pile. The diameter of the base of the cone is three times the altitude. Find an expression for the volume of the cone in terms of h, the height of the cone.

Question

anonymous · Answer

vol of cone = (1/3) pi r^2h
d = 3h
also d=2r
so 2r = 3h
r = 3h/2

so vol = (1/3) pi * (3h/2)^2 * h
           = 1/3  pi * 9h^3 / 4
            =  3pi h^3 / 4

anonymous · Answer

thanks a lot