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A 100 (US liquid) gallon cube is 23100 cubic inches. The maximum proportion of a cube which can be filled by spheres, using cubic closed packing or hexagonal close packing is approx 74.05%. Consequently, the spheres can occupy at most 17105 cubic inches. This volume implies a maximum of 335 spheres.

You cannot divided the volume of the cube by the volume of each sphere because spheres can never occupy all the space in any shape.

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Q: If I have a 2.3 inch in diameter sphere. How many spheres would it take to fill a 100 gallon cube?
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