Hollow cylinder region

Dear LAMMPS users,
I have a question regarding regions. I have spent a few hours trying to create a hollow cylinder, which I want to fill with water molecules. My goal is to place the water molecules in the layer between two coaxial cylinders of different radius.

My current approach is to define the innermost cylinder with side out, and the uttermost with side in, and then take the union of these two regions:

I think you don’t want the union but the intersection.