The diameter of a solid metallic right circular cylinder is equal to its height. After cutting out the largest possible solid sphere from the cylinder, the remaining material is recast to form a solid sphere . What is the ratio of the radius of the sphere S to that of sphere \(S_1\)?

A. \(\sqrt[3]{2:1}\)
B. \(\sqrt[3]{3:1}\)
C. \(\sqrt[3]3\)
D. None of these

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