Isovolume Problem

Find the surface enclosing the maximum volume per unit surface Area $I\equiv V/S$. The solution is a Sphere, which has

$$I_{\rm sphere}={{\textstyle{4\over 3}}\pi r^3\over 4\pi r^2}={\textstyle{1\over 3}}r.$$

See also Dido's Problem, Isoperimetric Problem

References

Bogomolny, A. ``Isoperimetric Theorem and Inequality.'' http://www.cut-the-knot.com/do_you_know/isoperimetric.html.

Isenberg, C. Appendix VI in The Science of Soap Films and Soap Bubbles. New York: Dover, 1992.