Calculating Work and Mass for a Conical Mound of Height h

[elitespart]

1. A great conical mound of height h is built. If the workers simply heap up uniform material found at ground level, and if the total weight of the finished mound is M, show that the work they do is .25hM

So I related weight density to mass by using volume of a cone and got $$w = \frac{3M}{R^{2}\pi h}$$.

I used "r" as the radius of dW. and I got r = xR/h (not sure if this part is right) which would make $$W = \int w(xR/h)^{2}\pi xdx$$ from 0 to h.

Where am I messing up? Thanks.

 

[Dick]

If you are using r=R*(x/h) then r=0 at x=0 and r=R at x=R. So 'x' is the distance from the top of the cone. The height (distance from the bottom of the cone) is then h-x. Replace the appropriate x in your integral with the height.

 

[elitespart]

Oh right. Thanks for your help.