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A hundred ton steel ship floats, a hundred ton steel block does not. Density equals weight per volume. If you increase the volume without increasing the weight, the density will go down.
Exactly my point, the volume doesn't change in the example provided. Weight and volume stayed the same. We either need to expand Godzilla or it needs to eject some mass.
I think that it’s implicit that the volume of Godzilla would increase; we need to assume that the bounding layer has a degree of elasticity and that that the matter displaced by the flotation cavity will expand into that, reducing the net density.
Mighty Godzilla, with power untold
Rises through the waves; his powers unfold
Hidden muscles in clever design
Create a new chamber as they realign
Inflating his body, a titanic display
Defying the depths, he floats up and away
No long bound by the oceans’s might
Godzilla soars, a triumphant sight!
Yes, that would work. But imagine the swelling, to give Godzilla that much buoyancy.
Ordinary biomatter is very close to the density of water to begin with. That's why having a little air in your lungs is enough to be the difference between sinking and floating.
If Godzilla's biomatter under 1atm of pressure has a density close to water then being able to compress or expand an empty chamber inside his body by even just a tiny percentage of his ordinary overall volume could be the difference between floating at sea level or sinking to extreme depths.
Or if you prefer we can imagine that Godzilla gives himself a big ole booty when he needs to come up to the surface and make a mess of things.
First, let's address the expansion of lungs, because you say "little air", but in terms of volume, lungs are very big. On average, the volume of a human body is about 65 liters. When person fully exhales, the lung capacity is at about 1-1.5L; when expanded, it's about 5-6L. Interpreted charitably, that's roughly 8% percent of the entire human body volume. So realistically, expansion of the body by 8% is the difference between slowly sinking, and floating with the top of your skull (or roughly 1% of your body volume) peaking out of water.
Now, Godzilla, on the other hand, has like 80% of his body above water. Can you imagine, the amount of expansion that needs to happen for that much buoyancy? That's pufferfish territory.
So no, a "tiny percentage" increase in body volume driven by empty chamber "inside" his body would not be enough.