MathDB

5

Part of 1974 IMO Longlists

Problems(1)

Geometric Inequality [ILL 1974]

Source:

1/2/2011
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 V1≤3πV227.V_1 \leq \frac{\sqrt 3 \pi V_2}{27}.
inequalitiesgeometry3D geometrygeometry unsolved