The concept of volume-to-surface area ratio (V/A) or its reciprocal is useful in thinking about basic metabolism, structure, and elementary biomechanics in the study of living organisms (and also the structure of inanimate objects). Unfortunately, for obvious reasons, such ratios are dimensional, i.e., either in units of length or its reciprocal in the examples mentioned; hence, the numerical value will depend on the units used.

A related but dimensionless measure of volume-to-surface area is the sphericity indexχ. This is defined as χ = αV2/3/A, where α is the constant such that for a sphere, χ = 1.

Estimate χ for the yucca plant in the picture. It is about 1 m in diameter.

Look for the answers online at tpt.aapt.org under “Browse,” at the very end of the current issue.

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