22. When a cube is cut into two pieces with a single plane cut, two polyhedra are obtained. Which of these polyhedra cannot be obtained in this way?
A A polyhedron with 4 faces
B A polyhedron with 5 faces
C A polyhedron with 6 faces
D A polyhedron with 7 faces
E A polyhedron with 8 faces
22. E The cube has six faces. When a single plane cut is made, it splits the cube into two polyhedra. Each of these will have all or part of some of the faces of the cube together with one new face. So it is not possible to produce a polyhedron with 8 faces. The first diagram below shows a cut which gives a polyhedron with 4 faces and a polyhedron with 7 faces. The second diagram shows a cut which gives two polyhedra, each with 5 faces. Finally, the third diagram shows a cut which gives two polyhedra, each with 6 faces.