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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


Bogomolny, A. ``Isoperimetric Theorem and Inequality.''

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

© 1996-9 Eric W. Weisstein