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UKMT Senior Mathematical Challenge, 2016

Geometry Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

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

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

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