Volume of a Pyramid

Take a box and a pyramid with the same square base and the same height. Fill the pyramid with sand and pour it into the box: it takes exactly three pyramids to fill it. A pyramid holds one third of the prism around it.

This pyramid has a square base 6 by 6, so the base area is ${6}^{2} = 36$. The box around it would hold $36\cdot 4 = 144$, and the pyramid holds a third of that: $\frac{1}{3}\cdot 36\cdot 4 = 48$.

The rule is Volume of a pyramid: $V = \frac{1}{3}\cdot {b}^{2}\cdot h$, a third of the base area times the height. The height is the dashed one inside, from the apex straight down to the centre of the base.