Try this. Take a few big carrots that just fit into a mason jar and cut them into thirds. Now slice them into strips that you would add to a salad. I doubt that you can get them back into that mason jar. Potatoes yield the same result.I guess it depends on who is stacking. The couple times I've taken a stack of rounds, split it and restated I had at best about the same amount, though usually less. The splits can be stacked tighter.
I've also done his with blocks of wood. The smaller pieces never fit back in because of the air space that they require. I once split a large round into 45 splits. Two of them would have yielded 90 splits. In no way could those 90 splits ever have displaced the same or less volume as the two big rounds and whatever air was between them.