[size=150]A sphere, a cone and a cylinder of same radius are cut by the same horizontal plane. The height of the cone and cylinder is equal to their radius. [br][br]We can compare their cross sections obtain from the height.[br] [br][list][*][size=150]Drag G to change the height of the cutting plane.[/size][/*][*][size=150]What do you notice? What do you wonder?[/size][/*][/list][br][/size]

[size=150]Regardless of the height of the cutting plane, the sum of sections from the sphere and cone is the equal to the section of the cylinder. [br][br]By the Cavalieri's Principle*, the volume of the cylinder should be equal to the sum of volume of the cone and the hemisphere.[/size][br][br]* [url=http://en.wikipedia.org/wiki/Cavalieri's_principle]http://en.wikipedia.org/wiki/Cavalieri's_principle[/url]