Centre of mass with variable density distibution p(z)=Az/R^4, "A" constant

[MAH505]

A solid, non uniform cone has radius, R, height h and density distibution p(z)=Az/R^4 where A is a constant. Find the position of the centre of this cone from its base.

I have attached the picture of my cone and my workings thus far.
My answer doesn't seem to be right however. (4/5h seems too high?)

Any help would be greatly appreciated

 

[tkhunny]

Limits: Just \(\displaystyle [0,h]\) -- Are you sure? That might be a Right Circular Cylinder.