the square cube law in biology

Question

Can anyone explain in simple terms the square cube law and how it applies to animals and people. I have seen it referenced to fictional beast, especially those who are absurdly large. But can anyone explain it what it actually means

In: Biology

Answer 1

Let’s simplify with a cube.

A cube has 6 square sides, so it’s surface area is 6*s*^(2), where *s* is the length of a side.

A volume is just *s*^3

So the surface area depends on the square of *s*, whereas the volume depends on the cube of *s*. Hence the name of the law.

This means volume gets bigger faster than the surface area. A 1x1x1 cube has a surface area of 6 and a volume of 1. A 100x100x100 cube has a surface area of 60,000 and a volume of *1,000,000*.

For living things, surface area and volume have different functions and effects.

For example, every cell in our body generates heat, but heat can only escape from our skin. Aka our volume creates heat, but our surface area removes heat. If we simply scale up a human, they’d likely just overheat because they can’t get rid of heat fast enough.

Another example is falling. More volume means more weight, obviously. But air resistance is based on surface area. That means bigger animals have a faster terminal velocity. An ant can survive any fall, but we’d get splattered from high falls.