Question 3
A tetrahedron is to be cut by three planes to obtain a parallelepiped whose three faces through one vertex lie on faces of the tetrahedron.
(a) Can the parallelepiped have volume $9/10$ of the tetrahedron's volume? Explain.
(b) Determine a common point of the three cutting planes so that the parallelepiped has volume $11/50$ of the tetrahedron's volume.
(a) Can the parallelepiped have volume $9/10$ of the tetrahedron's volume? Explain.
(b) Determine a common point of the three cutting planes so that the parallelepiped has volume $11/50$ of the tetrahedron's volume.