If a sphere contains this cuboid, what's the largest cube it can contain?

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A cuboid has sides of lengths \(22\), \(2\) and \(10\). It is contained in a sphere of the smallest possible radius. What is the side-length of the largest cube that will fit inside the same sphere?

(A) \(10 \quad\) (B) \(11 \quad\) (C) \(12 \quad\) (D) \(13 \quad\) (E) \(14\)