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
In: 0
The thing you’re forgetting is how area and volume related to the ability of some structure to hold its own weight.
Volume correlates with weight. Switching units of volume isn’t going to change its weight. You can’t make an object lighter or heavier by deciding to measure its volume in different units.
The internal strength of an object correlates with area (specifically cross-sectional area). Switching units of area isn’t going to change its strength. You can’t make an object stronger or weaker by deciding to measure its area in different units.
As an object increases proportionately, its volume (and therefore its weight) increases by the cube of that factor but its area (and therefore its strength) increases only by the square of that factor. So its weight increases much faster than its strength, meaning at some point its weight will exceed its strength.
Specifically your 1m^(3) object is about 35 times as heavy as your 1 cu. ft. object, but only about 11 times stronger.
Latest Answers