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Origin-Triangle Tetrahedron Volume

Source: AMC 12 2008A Problem 18

February 17, 2008
geometry3D geometrytetrahedronpyramidcalculusanalytic geometryarea of a triangle

Problem Statement

Triangle ABC ABC, with sides of length 5 5, 6 6, and 7 7, has one vertex on the positive x x-axis, one on the positive y y-axis, and one on the positive z z-axis. Let O O be the origin. What is the volume of tetrahedron OABC OABC? <spanclass=′latex−bold′>(A)</span> 85<spanclass=′latex−bold′>(B)</span> 90<spanclass=′latex−bold′>(C)</span> 95<spanclass=′latex−bold′>(D)</span> 10<spanclass=′latex−bold′>(E)</span> 105 <span class='latex-bold'>(A)</span>\ \sqrt{85} \qquad <span class='latex-bold'>(B)</span>\ \sqrt{90} \qquad <span class='latex-bold'>(C)</span>\ \sqrt{95} \qquad <span class='latex-bold'>(D)</span>\ 10 \qquad <span class='latex-bold'>(E)</span>\ \sqrt{105}
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