A cube is divided into six identical square pyramids, each with a perpendicular height (s) that is half the length of the base edge (2s). Show that the volume of each pyramid is one third the volume of a square prism with the same base edge and perpendicular height.

Answer 1

pyramid
... v = 1/3 (base area)(height)
... v = 1/3 * (2s)^2 * s = 4/3 s^3

prism
... v = l w h = 2s * 2s * s = 4 s^3