Here's the most satisfying demo in geometry. Take a cone and a cylinder with the SAME circle base and the SAME height. Fill the cone with water and pour it into the cylinder — it takes exactly three pours to fill it. Not roughly three: exactly three, every time. Pointy shapes hold a third of their straight-sided partners, and that third IS the formula: $V = \tfrac{1}{3}\pi r^2 h$ (read aloud: V equals one-third pi r squared h): $r$ is the cone's base radius, $h$ its straight-up height, the same two letters the cylinder used.

Pyramids play the identical game with their prism: $V = \tfrac{1}{3} B h$ — one-third base area times height — where $B$ is the base's area, whatever polygon it happens to be. The family has one house rule: never forget the third. An answer three times too big means your cone quietly became a cylinder while you weren't looking.