Why the big roast takes so long.
A cube's surface area grows with the square of its size but its volume grows with the cube, so smaller objects have far more surface for every unit of volume. That's why a roast twice as thick can take roughly four times as long to cook through — and why a mouse-sized animal loses heat, and needs to eat, far faster relative to its weight than an elephant.
Cube, drawn to true relative scale
Surface-to-volume ratio vs. size
Characteristic size L
A⁄V ∝ 1⁄L
2 cmdouble L · quarter the ratio · 4× the heat-through time300 cm
Surface-to-volume ratio
cm⁻¹
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For a cube of side L, surface area A = 6L² and volume V = L³, so the square–cube law gives A⁄V = 6⁄L — halving L doubles the ratio, doubling L quarters it. A real roast or animal isn't a cube; this is a scaling argument about shape in general, not a literal model of one. The heat-through-time readout is a separate, related fact: for roughly cube-shaped heat diffusion, the time for heat to reach the centre scales with L², not with A⁄V directly — so doubling a roast's thickness takes about four times as long to cook, even though its surface-to-volume ratio only halved. That L² relation is a simplified heat-diffusion approximation; real roasting time also depends on oven temperature, the meat's composition and starting temperature, and bone conduction, none of which are modelled here. The biology side is the same geometry read the other way: small warm-blooded animals have much more surface relative to their body volume than large ones, so they lose metabolic heat faster relative to their mass and must eat proportionally more just to stay warm — a real, general principle in animal size and shape (bordering on the territory of Bergmann's rule), kept qualitative here rather than attached to invented metabolic numbers.