Understanding the Square-Cube Law

The square-cube law states that as a shape grows in size, its volume grows __________ its surface area.

• At the same rate as

• Slower than

• Faster than

• Independently of

If the side length of a cube is doubled, by what factor does its surface area increase?

• 2

• 4

• 6

• 8

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CCSS.6.G.A.4

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CCSS.5.MD.C.5B

CCSS.6.G.A.2

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CCSS.6.G.A.4

The square-cube law has important implications in biology. Which of the following best explains why very large animals need proportionally thicker bones than smaller animals?

• Larger animals have less dense bones

• Volume (and thus mass) increases faster than cross-sectional area of bones as size increases

• Surface area increases faster than volume as size increases

• Larger animals have a higher metabolic rate per unit mass

A small insect can walk on water due to surface tension, but a large animal cannot. This phenomenon is best explained by the square-cube law because:

• Surface tension forces scale with volume, while weight scales with area

• Surface tension forces scale with length, while weight scales with volume

• Surface tension forces scale with area, while weight scales with length

• Surface tension forces and weight both scale with area equally

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CCSS.8.G.A.3