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1990 AMC 12 #25

Source:

December 30, 2011
geometry3D geometrysphereAMC

Problem Statement

Nine congruent spheres are packed inside a unit cube in such a way that one of them has its center at the center of the cube and each of the others is tangent to the center sphere and to three faces of the cube. What is the radius of each sphere?
<spanclass=′latex−bold′>(A)</span> 1−32<spanclass=′latex−bold′>(B)</span> 23−32<spanclass=′latex−bold′>(C)</span> 26<spanclass=′latex−bold′>(D)</span> 14<spanclass=′latex−bold′>(E)</span> 3(2−2)4 <span class='latex-bold'>(A)</span>\ 1-\frac{\sqrt{3}}{2} \qquad<span class='latex-bold'>(B)</span>\ \frac{2\sqrt{3}-3}{2} \qquad<span class='latex-bold'>(C)</span>\ \frac{\sqrt{2}}{6} \qquad<span class='latex-bold'>(D)</span>\ \frac{1}{4} \qquad<span class='latex-bold'>(E)</span>\ \frac{\sqrt{3}(2-\sqrt{2})}{4}
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