Probably just fairly bog standard geometry combined with some material science/engineering on the physical properties of the cardboard (such as how much it can compress/stretch)

• Geometry: this problem more or less boils down to a 2d analysis since we need merely to look at a circular cross section. You could calculate the area each roll takes up by calculating the outer circle area minus the hole’s area, then divide the hole area by the ring’s area to get a theoretical maximum. This is assuming the material cannot stretch or compress. Not sure if this has a name, but it probably does.

• Material science: Maybe you could measure the dimensions of a roll, stress test it in various ways, and re-measure the new dimensions to get a profile of how the cardboard warps. You could use that to get a better estimation of how much cardboard you can stuff into itself, but I’m not as sure on the details there.

The latter

With enough of those you could probably do some kind of epoxy pour and make a cool end table top.

Guests will be impressed by the amount you have pooped in the past.

What an impressive collection, one day it might be worth a fortune!

My wife goes through twelve rolls in a week.