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A quotation from J.B.S. Haldane's essay describes dividing an animal's length, breadth, and height each by ten. What happens to its weight and its surface area as a result?
ABoth weight and surface area fall to about one tenth of their original values
BWeight falls to about a thousandth while surface area falls to about a hundredth
CWeight falls to about a hundredth while surface area falls to about a thousandth
DNeither the weight nor the surface area changes at all in this scaling
Answer & Solution
Correct answer: B. Weight falls to about a thousandth while surface area falls to about a hundredth
1. Weight scales with volume, which scales with the cube of a linear dimension.
2. Dividing every linear dimension by ten divides volume, and therefore weight, by ten cubed, which is a thousand.
3. Surface area scales with the square of a linear dimension, so it is divided by ten squared, which is a hundred.
4. This matches exactly: weight reduces to a thousandth while surface area reduces only to a hundredth.
5. This is why a smaller animal feels relatively more air resistance for its weight than a larger animal does.
_Source: OpenStax College Physics (CC BY 4.0), Ch 5 "Further Applications of Newton's Laws: Friction, Drag, and Elasticity", section 5.2 Drag Forces_
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