



 
Tom, For problems involving a three dimensional object I find it helpful to have a physical model. A rectangular parallelepiped is a "box" and so I located a box in my office as a model for your first problem. The red dot identifies a vertex and the face with the printing does not contain the vertex. This face has two diagonals so there are two ways to cut the box. Here is one diagonal. Cutting the box by a plane containing this diagonal and the specified vertex cuts it along the red lines. This cuts the box into two pieces. Is either of the pieces a pyramid? What is its volume? What happens if you cut along the other diagonal? Penny
 


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences. 