Archimedes wrote nine treatises that survive. In On the Sphere and Cylinder, he showed that the surface area of a sphere with radius r is 4πr2 and that the volume of a sphere inscribed within a cylinder is two-thirds that of the cylinder. (Archimedes was so proud of the latter result that a diagram of it was engraved on his tomb.) In Measurement of the Circle, he showed that pi lies between 3 10/71 and 3 1/7. In On Floating Bodies, he wrote the first description of how objects behave when floating in water.
