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Archimedes' Method for Computing Areas and Volumes - Exercise on Proposition 4 of The Method

Author(s): 
Gabriela R. Sanchis

Investigate Archimedes' Proposition 4 below, which concerns a paraboloid (the solid obtained by rotating the curve x = y2 about the x-axis) inscribed inside a cylinder. A static version of the balancing appears below. If you click on Proposition 4, you will get a dynamic version.

a) Describe the balancing relationship that is illustrated in the sketch.

b) Use this relationship to determine a relationship between the volume of the paraboloid and the volume of the cylinder.

c) Find a formula for the volume of the paraboloid in terms of r, the radius of the cylinder.

Click here to get the solutions for this exercise.

Gabriela R. Sanchis, "Archimedes' Method for Computing Areas and Volumes - Exercise on Proposition 4 of [i]The Method[/i]," Loci (June 2010)

Dummy View - NOT TO BE DELETED