A paperweight is made from a glass cube of side 2 units by first shearing off the eight tetrahedral corners which touch at the midpoints of the edges of the cube. The remaining inner core of the cube is discarded and replaced by a sphere. The eight corner pieces are now stuck onto the sphere so that they have the same positions relative to each other as they did originally.
What is the diameter of the sphere?
Input note: give your answer as an exact value.
Select one option, then click Submit.
\sqrt{8} - 1
\sqrt{8} + 1
\frac{1}{3}(6 + \sqrt{3})
\frac{4}{3}\sqrt{3}
2\sqrt{3}
Select an option, then submit.
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Senior Mathematical Challenge 2007 (2007)
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