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 surface area to volume ratio is unit-independent, yes. But that doesn’t change the physical meaning of the ratio.
Say that for each cubic foot of living matter, you need 1 pound/min of oxygen. Each square foot can provide 0.3 pounds/min through it. For your 1ft cubic organism, you can provide 6×0.3=1.8 pound/min of oxygen, which is more than the 1 pound/min needed. Good.
Let’s go to the bigger cube. 1 meter = 3.3 ft. 1 cubic meter is 3.3^3 ~ 36 cubic ft, so 36 pound/min of oxygen needed. The surface can provide 6x(3.3×3.3)x0.3 = 19.6 pound/min of oxygen. Not good.
Just playing with units doesn’t change the inherent fact that volume is what determines cellular needs/uptake, while surface area determines nutrient/gas/excretion availability/rate. Since volume scales up faster than surface area, so too does cellular demand scale up faster than nutrient/gas availability.
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