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The sphere is the shape with the smallest surface for a given volume. to prove this...

The sphere is the shape with the smallest surface for a given volume. to prove this statement properly requires variational analysis. here we want to confirm this result only for a selection of highly symmetric shapes by calculating the ratio of surface to volume. find these ratios for each of these shapes. sphere, cylinder, cube,pyramid, tetrahedron, cone. does this statement hold for six shapes?

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