Moment of inertia for a cylinder at a distance from rotation axis

[pinodk]

Homework Statement

I have a cylinder, for which i want to find the inertia tensor.
http://www.mip.sdu.dk/~pino/inertiacyl.JPG
Where the rotational axis are either the x (red) or y (green).

Homework Equations

I know that the inertia tensor for a cylinder is of the form
http://www.mip.sdu.dk/~pino/inertiamoment-cylinder.jpg
Then I believe that the bottom right element stays the same, since this describes the rotation around the z-axis.
The tricky part for me is the rest of the matrix. I am no expert, and do not understand inertia tensors fully, so I would like some pointers.

The Attempt at a Solution

My immediate idea is that the matrix should remain in its diagonal form, the zeros will remain zeros, is this correct?

I know that for complex forms i can split up the moments of inertia, so i have the moment of inertia for the blank space d, which is 0. and then i can add the moment of inertia of the cylinder, but how do i calculate this, when the rotational axis is x-axis for example?

 

[pinodk]

I had a sudden struck of enlightment...
Is it really as simple as just taking d+h and and using as h in the matrix?