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Surface Area Increase by Size Reduction

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This Demonstration shows how breaking up a cube into smaller ones increases the total surface area.

Contributed by: Mark D. Normand and Micha Peleg (March 2011)
Open content licensed under CC BY-NC-SA

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Upon successive breakage into smaller cubes, each time by halving the sides, the volume remains constant while the surface area increases dramatically. The total area of all cubes at each iteration is the red dot on the continuous line plot of area/volume.

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