Cavalieri's Principle in 3D
Example 8. The formula for the volume of the sphere
In this construction the height of the cone equals the radius of its base and the radius of the sphere. The construction demonstrates that the sum of the volume of the hemisphere and the cone equals the volume of the cylinder with radius of the base and height equal to the same .
The proof has to be finalized by using the formulae for the volume of the cylinder and the cone.
More details.