The concept by which volumes are obtained as sums of sliced sections has been known for over two thousand years. The Chinese used the idea to develop formulae for well-known objects such as spheres and cones and, in particular, the mouhefanggi, that volume common to two intersecting cylinders.

The process is also ideally suited to the implementation on a spreadsheet and can be used as an excellent introduction to the process of integration.

SECONDARY: areas and volumes of general trapezoidal approximations; Chinese section theorem.

SIXTH FORM: plus areas and volumes using calculus.