Calculating Inertia Tensor of Hollow Cone

[esradw]

I need to find the inertia tensor for a uniform thin hollow cone,spinning about its ponted end.

When the cone is solid then everything goes very smoothly by using cylindrical polar coordinates. But how should I find if it is a hollow cone. To be able to write the density of the cone I have to use the area of the cone and when I want to find ( Izz ) I need to write the dm=density.dv but how am I going to write the dA in cylindrical polar coordinates . If I could find the Izz then I could jump into finding of Iyy and Ixx and the products of inertia must be 0 because of the symmetry.

please help
thanks

 

[Physics Monkey]

You can easily find the result for a spinning ring of a certain radius. Try breaking the hollow cone up into a series of rings and integrating.