It’s used in two contexts.
One is literal to the namesake: as an object grows, it’s surface area grows as a square of diameter, while volume grows as a cube. This is important for heat generation and retention of organisms, as the heat is generated by the bulk (volume) of the body, but absorbed or expelled by the skin (surface). This means that as an animal grows larger, it retains heat better, but conversely also has trouble shedding it.
In other words, mice freeze really easily, while elephants overheat (if not for evolved adaptations).
The other one is a bit more tangential, but relevant to ***everything***. The volume increases with the cube of diameter. And that means mass does too. This means the mass of an object increases far faster than its dimensions would suggest, and that also means it can quickly outgrow the strength of the materials it’s made of. That’s why you can make a tiny toy bridge out of playdoh, but won’t even be able to finish building a life sized one without it collapsing on itself.
The same goes for animals, their bones, sinews etc. are stronger compared to the body weight for a small animal than a big one. That’s why a ferret can fall on its head from many times it’s body length and be fine, but a human falling on their head from even literally the same height (not to mention one proportionally scaled) will get injured.
For particularly large animals, say elephants or dinosaurs, their bones have to grow ridiculously thick compared to their body size to not snap under their body weight. And for particularly ridiculous fictional creatures, they just simply cannot be made from real life flesh and bone, because there’s no way they wouldn’t collapse on themselves.
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