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Its volume would be multiplied by the cube of 2 and become 8 m 3. The original cube (1 m sides) has a surface area to volume ratio of 6:1. The larger (2 m sides) cube has a surface area to volume ratio of (24/8) 3:1. As the dimensions increase, the volume will continue to grow faster than the surface area. Thus the square–cube law.
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The ratio between the volumes of similar figures is equal to the cube of the ratio of corresponding lengths of those figures (for example, when the edge of a cube or the radius of a sphere is multiplied by three, its volume is multiplied by 27 — i.e. by three cubed). Galileo's square–cube law concerns similar solids.
Some of the economies of scale recognized in engineering have a physical basis, such as the square–cube law, by which the surface of a vessel increases by the square of the dimensions while the volume increases by the cube. This law has a direct effect on the capital cost of such things as buildings, factories, pipelines, ships and airplanes. [b]
"On Being the Right Size" is a 1926 essay by J. B. S. Haldane which discusses proportions in the animal world and the essential link between the size of an animal and these systems an animal has for life. [1]
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I noticed that in the wikipedia entry for this law (Square-cube law), no proof of the law is given. I would like a proof that the ratio of the areas and volumes of 2 similar figures is the square and cube of their scale factor respectively. Thanks. 175.156.52.140 00:06, 1 January 2015 (UTC) I think you can just prove that visually.