Microscopy & measurement · SL/HL

Surface area : volume

Compare surface area and volume for simple shapes.

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Number formats & units

Use decimal dots in datasets. Single values also accept decimal commas and scientific notation such as 1.2e-3 or 1.2 × 10⁻³.

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Example

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\text{cube:}\quad\mathrm{SA}=6a^2,\quad V=a^3

\text{sphere:}\quad\mathrm{SA}=4\pi r^2,\quad V=\frac43\pi r^3

\text{cylinder:}\quad\mathrm{SA}=2\pi r^2+2\pi rh,\quad V=\pi r^2h

\mathrm{SA}:V=\frac{\mathrm{SA}}V

What the variables mean

Symbol	Meaning
$\mathrm{SA}$	Surface area.
$V$	Volume.

SA:V = 3:1

Follow the example steps

Surface area and volume scale with different powers of length.

L → 2L: SA/V → 2SA/V

SA/V = 6/L; L → 2L: SA/V → 3/L

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Method notes

SA:V is a geometric comparison; biological exchange also depends on membranes, gradients, transport and metabolic demand.