Axial Tomographies (TACs) of Three-Dimensional Geometric Bodies

As do doctors, could we interpret the following TACs of geometric bodies and deduce what body they correspond to and which axis is perpendicular to the successive cuts?

Based on a Twitter conversation with Anton Aubanell and Bernat Ancochea, inspired by the work of Sir Godfrey Hounsfield, who invented the computed tomographic scanner, and thus made an incomparable contribution to medicine. This is my first attempt. I think it would be useful for a class discussion, after students investigate in their own way, but it does too much for them to be used as an exploratory tool.