Problem #PRU-111417

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

Problem

The height \(SO\) of a regular quadrilateral pyramid \(SABCD\) forms an angle \(\alpha\) 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 \(SO\). Find the volume of the common part of these pyramids.