2001 AIME II Problems/Problem 15

Problem

Let $EFGH$ , $EFDC$ , and $EHBC$ be three adjacent square faces of a cube, for which $EC = 8$ , and let $A$ be the eighth vertex of the cube. Let $I$ , $J$ , and $K$ , be the points on $\overline{EF}$ , $\overline{EH}$ , and $\overline{EC}$ , respectively, so that $EI = EJ = EK = 2$ . A solid $S$ is obtained by drilling a tunnel through the cube. The sides of the tunnel are planes parallel to $\overline{AE}$ , and containing the edges, $\overline{IJ}$ , $\overline{JK}$ , and $\overline{KI}$ . The surface area of $S$ , including the walls of the tunnel, is $m + n\sqrt {p}$ , where $m$ , $n$ , and $p$ are positive integers and $p$ is not divisible by the square of any prime. Find $m + n + p$ .

Solution

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2001 AIME II (Problems • Answer Key • Resources)
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2001 AIME II Problems/Problem 15

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