What if you put a smaller Gabriels Horn inside a larger one?

Okay chat let me cook. I have a thought experiment about Gabriel's Horn that is really confusing me. As I understand it, the inside of the horn is finite, but the outside surface is infinite.

What would happen if you were to take a smaller Gabriel's Horn and place it completely inside a larger Gabriel's Horn?

Wouldn't the inside of the larger horn be finite, and yet it somehow has to be larger than (or at least contain) the infinite surface of the smaller horn? How does that make sense?

Author: RideNatural5226