Use the fact that it takes three pyramids with sand to fill the prism to find a relation between the volumes.
The volume of the pyramid is one-third the area of the base multiplied by the height.
Practice makes perfect
In Exploration 1 we considered a pyramid and a prism with the same height and the same square base.
We also saw that to fill the prism with sand we had to fill and pour the pyramid three times. This implies that the volume of the prism (the amount of matter that it can contain) is three times the volume of the pyramid.
3* V_(pyramid) = V_(prism)
⇓
V_(pyramid) = 1/3V_(prism)
The volume of the prism is the area of the base multiplied by the height and the pyramid has the same base and height, so we conclude that the volume of a pyramid is one-third the area of the base multiplied by the height.
V_(pyramid) = 1/3Bh
