Problem #PRU-111417

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

13–15 3.0

Problem

The height $S O$ of a regular quadrilateral pyramid $S A B C D$ forms an angle $α$ with a side edge and the volume of this pyramid is equal to $V$ . The vertex of the second regular quadrangular pyramid is at the point $S$ , the centre of the base is at the point $C$ , and one of the vertices of the base lies on the line $S O$ . Find the volume of the common part of these pyramids.

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