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If the cells are spherical, the surface area increases as the square of the radius while the volume increases as the cube of the radius. Therefore, as the cells become larger, their volumes increase much more rapidly than their surface areas. Conversely, as the cells become smaller, their volumes decrease much more rapidly that their areas and so the surface area to volume increase.

With non-spherical cells the calculations are much more complex, but the general pattern still applies.

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Q: Why do smaller cells have a greater surface area to volume ratio?
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