MathDB
Geometric Inequality [ILL 1974]

Source:

January 2, 2011
inequalitiesgeometry3D geometrygeometry unsolved

Problem Statement

A straight cone is given inside a rectangular parallelepiped BB, with the apex at one of the vertices, say TT , of the parallelepiped, and the base touching the three faces opposite to T.T . Its axis lies at the long diagonal through T.T. If V1V_1 and V2V_2 are the volumes of the cone and the parallelepiped respectively, prove that V13πV227.V_1 \leq \frac{\sqrt 3 \pi V_2}{27}.