Hi Becky,

The volume of a pyramid is 1/3 × (the area o the base) × (the height). I don't know an intuitive way to demonstate why the fraction 1/3 appears. It follows from a much more general result that Bruce mentioned at the bottom to his response to an earlier question. I can show you in one particular case why the 1/3 appears.

If the pyramid has a square base with side length x and the height of the pryamid is x/2 then you can put 6 of these pyramids together to form a cube as in the diagram below.

The volume of the cube is x³ and hence the volume of the pyramid is 1/6 x³. But

1/6 x³ = 1/3 × x² × (1/2 x) = 1/3 × (the area of the base) × (the height).

Penny