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Difference between revisions of "Mock AIME II 2012 Problems/Problem 13"

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Revision as of 03:21, 5 April 2012

Problem

Regular octahedron $ABCDEF$ (such that points $B$, $C$, $D$, and $E$ are coplanar and form the vertices of a square) is divided along plane $\mathcal{P}$, parallel to line $BC$, into two polyhedra of equal volume. The cosine of the acute angle plane $\mathcal{P}$ makes with plane $BCDE$ is $\frac{1}{3}$. Given that $AB=30$, find the area of the cross section made by plane $\mathcal{P}$ with octahedron $ABCDEF$.

Solution

There is currently no solution to this problem. If you discover one, please update this to the solution. You can check your answers with the answer key provided on the Mock AIME II 2012 Page.

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