SPHERE, CYLINDER & CUBE

Consider a cylinder of height R and base radius also R, a cone with equal base and height and a sphere of radius R. The result that fascinated Archimedes was that the volume of the cylinder pR³ fwas the sum of the volume of the cone 

1/3  pR³  

and the volume of the sphere

4/3  pR³

What is the relationship between a sphere of radius r and the cone with radius r and height r?

Spheres & ellipsoids

Index

A sphere as isogonal surface