how to shoot this (cylindrical room)
You need a giant telecentric lens!!!
There are two or three ways to render the depth. Stereoscopy, putting an object with standard recognisable proportions as a reference or suggesting it with lighting. For fun purpose, and I'm sure Sailor Blue would say the same, a 3D set would be great for this.
Or else, you can put a graded lighting that goes darker as you go deeper in the corner on one side.
And for the object of known proportions, you can stand a beatiful naked woman in the bath and show how high and deep the room is compared to this known reference! Or a mix of the three techniques!