Volume of a Sphere

1. Use a method similar to that of Archimedes to derive the formula for the volume of a cone as being 1/3 that of the cylinder with the same base and height.
2. The ancient mathematicians, such as Archimedes and Euclid, often related characteristics of more complex 3-D objects to that of more simple 3-D objects. Archimedes' discovery that a sphere has the same volume of as the volume of cylinder with the same height and radius minus the volume of two cones each with the same radius and half the height is a good example of this point. Can you think of any other 3-D objects that you could relate in a similar fashion. (Hint: Question 1 should expose such a relationship)

Paul Clayton, 25 November 2013, Created with GeoGebra