hollowing out a ring

 From:  Rudy
Dear all,
I am trying to figure out a way to hollow a ring with the hollowed area having the same contour of the original ring.
see attachment.
In my file, There is the orignal tapered ring and then a smaller ring (B) which was thinking to insert in the original ring, and doing a boolean difference

((I think Rhino does this by offset the original contour, then using different layers, and extruding both solid within each other, and at the end boolean difference. (I saw this on the first and only one tutorial I apprached)).

I am trying this way, but it looks it doesn't work so far....
Can anybody help me on this.
Is it possible to realize an idea like this?
Am I doing the wrong approach?

Thank you,