If a solid metallic sphere of radius $8$ cm is melted and recasted into $n$ spherical solid balls of radius $1$ cm, then $n$ is:

Because the volume remains unchanged when the metallic sphere is melted and recast, the volume of the large sphere equals the total volume of the n small balls. Using the sphere volume formula, four thirds times pi times 8 cubed equals n times four thirds times pi times 1 cubed. Solving for n gives n equals 8 cubed, which results in 512.

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