6.2 On the Sphere and Cylinder
Cicero has related that when serving as Roman quaestor in Sicily he found and repaired Archimedes’ then neglected (but now vanished) tomb,upon was engraved a sphere inscribed in a cylinder. This device com-the memorates Archimedes’ favorite work, On the Sphere and Cylinder. Verify the following two results established by Archimedes in this work: (a) The volume of the sphere 2/3 that of the circumscribed cylinder. (b) The area of the sphere is 2/3 of the total area of the circumscribed ctlinder. (c) Define stherical zone (of one and two bases), spherical segment (of one and two bases), and spherical sector.