Double every dimension of a shape and its area quadruples while its volume grows eightfold — the exponent, not the shape, decides how fast size compounds.
This is why small animals lose heat faster relative to their mass (surface area) than large ones, and why doubling a tank’s dimensions needs eight times the material to hold eight times the liquid, not twice.
Only under uniform scaling. Stretch one dimension and the exponents no longer apply. It is also why scale models mislead: doubling an animal's height multiplies its weight eightfold but its bone cross-section only fourfold, which is the reason a mouse enlarged to elephant size would collapse.
Estimate with the rule, then check it against the calculator that models it properly.
Open Geometry — 2D & 3D →Double every dimension of a shape and its area quadruples while its volume grows eightfold — the exponent, not the shape, decides how fast size compounds. This is why small animals lose heat faster relative to their mass (surface area) than large ones, and why doubling a tank’s dimensions needs eight times the material to hold eight times the liquid, not twice.