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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You’re not using units quite right. You have to compare apples to apples. Let’s use two different units to prove this:
You have a one meter cube. You double its size, and have a two meter cube. Its surface area goes from 6 square meters to 24. Its volume goes from 1 cubic meter to 8. Its volume has increased twice as much as its surface area.
Same cube, let’s use feet instead. 3.28 feet is one meter. The 1M cube has a side length of 3.28 feet. This makes for a surface area of 64.55 square feet, and a volume of 35.287 cubic feet. Scale it up, just like last time, to a side length of 6.56 feet. SA is now 258.2 square feet. Volume is 282.3 cubic feet. If we compare the two, we see that the volume has increased twice as much as the surface area.
This holds true for any unit you choose, so long as you don’t goof up the math during your conversions. The most common such error is forgetting to square during unit conversions. Example:
1 square foot = 12 square inches. This is wrong. A foot is 12 inches, so a square foot is (twelve squared) square inches, or 144 square inches.
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