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Biology — Surface Area : Volume

SA:V ratios for a cube and sphere and why size limits exchange.

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\frac{SA}{V} = \frac{6}{l}\;\;\text{(cube)}

\frac{SA}{V} = \frac{3}{r}\;\;\text{(sphere)}

SA = 4\pi r^2, \quad V = \tfrac{4}{3}\pi r^3

\text{exchange rate} \propto \frac{SA}{V}