Final answer:
A cube can have triangular, hexagonal, and square cross sections; a right square pyramid can have trapezoidal and square cross sections; a square cross section is common to both shapes but a hexagonal cross section is not possible in both.
Step-by-step explanation:
When considering the possible cross sections of a cube and a right square pyramid, we find that multiple shapes can be achieved depending on the plane of the cut. Starting with the cube:
- a. Triangular cross section from the cube is possible if you slice it diagonally from one edge to the opposing edge within the same face.
- d. Hexagonal cross section from the cube can be obtained if you slice through all six vertices.
- g. A square cross section can be easily achieved by slicing the cube perpendicular to any of its faces.
For the right square pyramid:
- b. A trapezoidal cross section can be sliced if a cut is made parallel to the base, but not intersecting it, and below the apex of the pyramid.
- e. Square cross section can be taken right at the base of the pyramid.
Considering both the cube and right square pyramid:
- f. A hexagonal cross section is not possible for both because a pyramid does not have the necessary six vertices on a single plane like a cube does.
- g. A square cross section is common to both only at the base of the pyramid and anywhere on the cube if sliced perpendicularly to its faces.