1 Death of Insanely Overpowered Fireballs: Okay, we have instruments. Time to put out the hat.
2 Death of Choking on a Giant Frog: I’m very curious as to what’s beneath your top hat.
3 Death of Inhaling Hatmaking Chemicals: Ett vie-ola, guv. {Death of Inhaling Hatmaking Chemicals takes his hat off, revealing... another identical hat beneath it}
4 Death of Choking on a Giant Frog: That’s both kind of disappointing and kind of fascinating.

Cat in the Hat, eat your heart out.

I always did wonder how all those little cats fit under there.

Measuring a handy illustration of the Cat in the Hat, the relative proportions of the Cat and his hat are:

Cat: 150 mm tall
Hat: 37 mm tall

If we assume the original Cat in the Hat is, say 150 cm tall, with a 37 cm hat, and the hat material is of negligible thickness, then each sub-cat is 37/(150+37) the height of the previous cat. Little Cat Z is then (37/187)²⁶ times as tall as Cat Prime, which turns out to be 5.1×10^-19 times 150 cm, which is 7.6×10^-19 metres tall.

This is much smaller than the nominal radius of a hydrogen atom (5.3×10^-11 m), and about 1000 times smaller than the root mean square radius of the charge density (the best estimate of the "size") of a proton, which is 8×10^-16 m.

One may reasonably conclude that Voom is some sort of metastable quark-gluon plasma.

Note: It's difficult to get a really good idea of how the sizes of each cat scale, as the images in the book are self-inconsistent. Not to mention that the Cat saunters in at full stretch with his hat handily under the door frame at the beginning of The Cat in the Hat, while at the end he has to stoop to clear it without bumping his head, and his hat scrapes the frame. Clearly this Cat is not only messing with quantum energies that are best left alone, but also with the very laws of geometry themselves.

Kids, you've been warned.