Archimedes's Tomb

Archimedes asked for a representation of a cylinder circumscribing a sphere on his tomb. Also his result on the ratio of the volumes of the two should be noted. He was proud of his discovery regarding the volume of a sphere, showing that it is two-thirds the volume of the smallest cylinder that can contain it. The volume of a cylinder of radius and height is ; the volume of a sphere of radius is . Furthermore, the volume of a bicone is half that of the smallest sphere that can contain it. Therefore these three volumes behave as 1 : 2 : 3.

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Related Curriculum Standards

US Common Core State Standards, Mathematics