A Sliding Cross-Section

★ 8/10Extrema Substitution solid geometry vectors

Problem

Let $P\text{-}ABCD$ be a regular quadrilateral pyramid with height $3$ and base edge $2$ , and let $M$ be the midpoint of edge $PC$ . A plane through $A$ and $M$ meets segments $PB$ and $PD$ at points $E$ and $F$ respectively (endpoints allowed). Find the maximum and minimum volumes of the pyramid $P\text{-}AEMF$ .

Answer

Solution

Difficulty	8/10
Topics	Extrema, Substitution, solid geometry, vectors

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