Disclaimer: I did see a previous question touching on something like this but what I’m confused about was NOT addressed so hopefully this is allowed.
They say that the surface area volume ratio limits how big things can grow because surface area scales as a square while volume scales as a cube, so the ratio of volume to surface area goes up as you get bigger. Fair enough. BUT: how is this not just a matter of what units you’re using?
For example, a 1x1x1 ft cube has a surface area to volume ratio of 6sq. Ft to 1 cubic foot, so 6:1. A 1x1x1 meter cube has a ratio of 6:1 too but the units are meters. Couldn’t you always define your units so that you have a 6:1 ratio with any size of cube?
To bring it back to the actual question, wouldn’t your ratio be essentially the same no matter how big your object is? Imagine you expanded everything in the universe by the same amount but kept your unit of measurement the same, you wouldn’t suddenly hit some limit where it stops working right? Does it have something to do with the size of molecules and proteins etc? Please help I am so confused
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The problem is that the ratio changes as the volume grows, even if you stick with the same units. A 1x1x1 meter cube has a 6:1 ratio, yes, but if we give the cube twice the volume (so it’s a 1.26×1.26×1.26 meter cube now, roughly), then its surface area ends up around 9.5, so the ratio is now something like 4.76:1
Sure, you can say “yes, but if I make up another unit then the ratio between *those* units is what I want it to be”, but that doesn’t change the fact that as the object grew, the ratio between volume and surface changed.
Physics doesn’t care which unit you choose to use. It cares that “compared to when the object was smaller, it now has a smaller surface to volume ratio”
The problems this causes are varied, but it’s not as simple as “suddenly the molecules in my body magically stopped working”. A few examples I can think of are:
1. because elephants are so big, they have volume many, may times greater than that of a human, but their surface area isn’t *as much* greater. This means they already have trouble cooling off. They generate heat throughout their massive bodies, but the heat can only escape through their skin, and compared to how big they are, they don’t have *that* much skin. So if you made an elephant with twice the volume, it would produce twice the heat, but it would not have twice the surface area from which that heat could escape. It would die.
Airplanes would also have problems if you just made them twice as big without changing anything else. Because their volume (and their weight) would double, but the surface area of the wings would not. The wings would need to be made *even bigger*. And of course, even bigger wings would suffer greater stresses and would need to be made stronger.
Plants can only absorb sunlight through their surface area. So if the volume of a plant doubled, but its surface area didn’t, it’d suddenly get relatively less sunlight than it did before.
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