Problem 331

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Problem 331: (2008 AMC 12a, 18)

A triangle $\triangle ABC$ with sides $5$, $6$, $7$ is placed in the three-dimensional plane with one vertex on the positive $x$ axis, one on the positive $y$ axis, and one on the positive $z$ axis. Let $O$ be the origin. What is the volume of $OABC$?

$\mathrm{(A)}\ \sqrt{85}\qquad$ $\mathrm{(B)}\ \sqrt{90}\qquad$ $\mathrm{(C)}\ \sqrt{95}\qquad$ $\mathrm{(D)}\ 10\qquad$ $\mathrm{(E)}\ \sqrt{105}$

Solution

Exercise 331: Solution

A triangle $ABC$ with $AB=BC=5$ and $CA=6$ is placed in space with $A$ on the positive $x$-axis, $B$ on the positive $y$-axis, and $C$ on the positive $z$-axis. Let $O$ be the origin. What is the volume of tetrahedron $OABC$?

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