Volume Of A Cone

Cones can be approximated by stacks of cylinders:

For a cone of radius r and height h, N cylinders would each have a height of approximately h / N. The set of approximate cylinder radii would be r / N, 2r / N, 3r / N, ..., r. The approximate volume of all the cylinders would be πr²h(1 + 4 + 9 + ... + N²) / N³. As N increases, the volume approximation improves and (1 + 4 + 9 + ... + N²) / N³ approaches 1 / 3. Therefore, the volume of a cone of radius r is πr²h / 3.