volume of a pyramid

a ppt is here

three methods to demonstrate that a pyramid is one third of the surrounding cuboid

[ the middle version (6 pyramids meeting at the centre of a cube) might be the easiest to understand but the other two methods generalise, from a cube to any cuboid ]

geogebra applet showing how the three pyramids make up the cuboid

you can vary each of the three dimensions

suppose each of the pyramids is the same fraction (f) of the surrounding cuboid