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Which has a greater surface area, a sphere or a cube?

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The cube of the same volume as a sphere of radius $r$ has side-length $r \cdot \left(\frac{4}{3}\pi\right)^{1/3}$ and thus surface area $6 \cdot r^2 \cdot \left(\frac{4}{3}\pi\right)^{2/3}$. Since $ 6 \left(\frac{4}{3}\pi\right)^{2/3} \approx 15.6$ is bigger than $4 \pi \approx 12.6$ the answer is: The cube. read more

The question is not correctly phrased. Comparison of the surface area of a cube and that of a sphere is only meaningful, when both bodies have the same volumes. The absurdity of the comparison has been illustrated in an answer by comparing the surface area of the the moon and an ice cube. read more

However, if you have a known volume, and want to contain it in either a cuboid or a cylinder, reducing the amount of surface area, then we're in business. Let's assume V = 1000. The most efficient cuboid is one where all the sides match, so S1 = S2 = S3 = 10. Volume 1000, surface area 600, with a ratio of 5/3 (1.6666). read more

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