Find the surface enclosing the maximum volume per unit surface Area . The solution is a Sphere, which
has
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.