Archimedes's Tomb

Archimedes's tomb

volume: 1 : 2 : 3

sphere
cylinder

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

C

of radius

r

and height

2r

is

2rπ×

2

r

=2π

3

r

; the volume of a sphere

S

of radius

r

is

4

3

π

3

r

. 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.