Intersecting Cylinders with Hollow Middle (AR Modeling Challenge)

The goal of this GeoGebra Augmented Reality modeling challenge is to construct 2 cylinders that intersect, yet have a hollow middle. In the screencast below, each right circular cylinder has radius = 1. The lines that pass through and serve as axes for both these cylinders. How can we construct such a surface by authoring only 2 surface equations?

Quick (Silent) Demo