Surface area scales with the square of a characteristic linear dimension while volume scales with the cube of that dimension, so as an object (such as a bacterium) gets smaller, its surface-area-to-volume ratio (S/V) increases; conversely, larger organisms/cells of the same shape have progressively smaller S/V ratios. This is why smaller bacteria have a proportionally larger cell-surface area relative to their internal volume compared to larger bacteria of the same species/shape.
For geometrically similar shapes, surface area S is proportional to the square of a linear dimension L (S is proportional to L^2), while volume V...
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