MathDB

A tetrahedron is to be cut by three planes which form a parallelepiped whose three faces and all vertices lie on the surface of the tetrahedron. (a) Can this be done so that the volume of the parallelepiped is at least

\frac{9}{40}

of the volume of the tetrahedron? (b) Determine the common point of the three planes if the volume of the parallelepiped is

\frac{11}{50}

of the volume of the tetrahedron.

Problem Statement