Problem #PRU-111415

Problems Calculus Real numbers Integer and fractional parts. Archimedean property Methods Pigeonhole principle Pigeonhole principle (angles and lengths)

13–15 3.0

Problem

The volume of the regular quadrangular pyramid $S A B C D$ is equal to $V$ . The height $S P$ of the pyramid is the edge of the regular tetrahedron $S P Q R$ , the plane of the face $P Q R$ which is perpendicular to the edge $S C$ . Find the volume of the common part of these pyramids.

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