Volume of a pyramide
Starting from a pyramid with a heigth that equals only half of the height of the cube, we even don't have to deform the pyramids to find a relationship between the volume of a cube and a pyralid.
Let s be the length of the side of a cube. In the applet we can see that the volume of a pyramid with a square base and a height that equals half of the the heigth of the cube can be calculated as V = 1/6 . s³
In the opposite way we can say that you an divide a cube into 6 equal pyramids.
as a formula for the volume of a pyramid we find:
| 6 . I | = s³ |
| I | = 1/6 . s³ |
| I | = 1/3 . s² . 1/2 . s |
| I | = 1/3 area base . heigth |