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Points Equidistant From a Line Segment

Source: 2017 AMC 10A #11, AMC 12A #8

February 8, 2017
AMCAMC 122017 AMC 10A2017 AMC 12A3D geometryAMC 10

Problem Statement

The region consisting of all points in three-dimensional space within 33 units of line segment AB‾\overline{AB} has volume 216π216\pi. What is the length ABAB?
<spanclass=′latex−bold′>(A)</span> 6<spanclass=′latex−bold′>(B)</span> 12<spanclass=′latex−bold′>(C)</span> 18<spanclass=′latex−bold′>(D)</span> 20<spanclass=′latex−bold′>(E)</span> 24<span class='latex-bold'>(A)</span>\ 6\qquad<span class='latex-bold'>(B)</span>\ 12\qquad<span class='latex-bold'>(C)</span>\ 18\qquad<span class='latex-bold'>(D)</span>\ 20\qquad<span class='latex-bold'>(E)</span>\ 24
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