Which books did Archimedes write about spheres and cylinders?

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Archimedes wrote the treatise titled On the Sphere and Cylinder, which consists of two books.12

In this work, he established significant mathematical proofs regarding the properties of these shapes, most notably demonstrating that:

  • The surface area of a sphere with radius r is four times the area of its greatest circle (S=4πr2).12
  • The volume of a sphere is two-thirds the volume of the cylinder in which it is inscribed (V=43πr3).12

Archimedes held these discoveries in such high regard that he requested a diagram of a sphere inscribed within a cylinder be engraved upon his tomb.12