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Figure 1. A sphere has 2/3 the volume of its circumscribing cylinder. The radius of the sphere is r.
Figure 2. Sphere, cylinder and cone.
Conclusion:
2 V3 = V2 3 Remark: If we know - as Archimedes did (McKeeman (2012)) - the signification of π,
2 4 3 V2 =2r (πr ) and consequently V3 = πr . 3
REFERENCES Calinger, Ronald. ”A Contextual History of Mathematics” p. 150. Prentice-Hall, ISBN 0-02- 318285-7. Shortly after Euclid, compiler of the definitive textbook, came Archimedes of Syracuse (ca. 287 – 212 BC), the most original and profound mathematician of antiquity (1999). Rorres, Chris. ”Tomb of Archimedes Illustrations”. Courant Institute of Mathematical Sciences (2011). McKeeman, Bill. ”The Computation of Pi by Archimedes”. Matlab Central (2012).