Problem #PRU-111415

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

Problem

The volume of the regular quadrangular pyramid \(SABCD\) is equal to \(V\). The height \(SP\) of the pyramid is the edge of the regular tetrahedron \(SPQR\), the plane of the face \(PQR\) which is perpendicular to the edge \(SC\). Find the volume of the common part of these pyramids.