For the inner cardboard tube, I didn't start the same way as with the roll of paper towels itself; I started with an extruded helix shape because those inner rolls have a spiral detail to them, so I needed a spiral edge, and this was one of the easiest ways to get it:

Then, I grabbed that spiral edge, chamfered it a little, and pushed it in some, like this:

After dding thickness, and a level of subdivision, I ended up with something that looks like those inner cardboard tubes:

Then I just added a cardboard texture to it:

Here it is all put together:

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