The “Square Cube Law”
In: Mathematics
Surface area goes up by a power of two, volume goes up by a power of three. Think about a cube with side length l. The surface area is 6l^2 and the volume is l^3. So for a unit cube surface area is 6 and volume is 1. At l=2 we get 24 and 8. L=3 is 54 and 27. L=4 is 96 and 64. L= 10 gives you 600 and 1000. As you can see, volume increases much quicker than surface area. This has very serious implications in engineering, because certain phenomena, like heat transfer, are dictated by surface area and are acting on volume. So if the system gets too large, cooling it down in any sort of meaningful amount of time can become deeply non-trivial.
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