Work problem: Find work done in building conical mound

[msl1333]

A great conical mound of heigh h is bulit by heaping uniform material found at ground level. If the total weight is M, show that the work they do is (1/4)hm.

I know that work is the integral of F(x) dx where F(x) is the force, and the volume of a cone is 1/3 pi*r squared*h...what I did was to imagine a slice of the mound of height dx, and at a height x from the ground, but I can't formulate it into an equation for the integral.

 

[Deleted member 4993]

Re: Work problem

A great conical mound of heigh h is bulit by heaping uniform material found at ground level. If the total weight is M, show that the work they do is (1/4)hm.

I know that work is the integral of F(x) dx where F(x) is the force, and the volume of a cone is 1/3 pi*r squared*h...what I did was to imagine a slice of the mound of height dx, and at a height x from the ground, but I can't formulate it into an equation for the integral.

Where is the center of mass of this cone?

You can estimate the work by assuming that the whole weight of the cone was lifted to CM from the ground.