moment of inertia

[Antares]

I need help finding the moment of inertia for a hollow cylinder with a closed bottom (like a glass of water). My strategy is to add the moments of inertia of the cylinder and the disk but I only have the total mass of the whole object. Is there a way to find the mass of each part or is there another approach to this problem?

[Kurdt]

Just sum the mass as an integral as follows.

I=\int r^2 dm

[Doc Al]

Is there a way to find the mass of each part or is there another approach to this problem?
If the thickness is uniform then you can find the masses of the cylinder and bottom by comparing their relative areas. The surface area of the cylinder is Lx2πr; the area of the bottom is πr2.