Variational calculus : A drop of water

Hi, anyone observed a drop of water before and noticed that while
falling, it is supposed to be spherical?

I know that it is a sphere but I need to prove it using variaional
calculus. Anyone got any hints?

Also, what good book are there on these kind of isoperimetric
problems?

I've got a book by I.M. Gelfand and Fomin, but it doesn't cover this
problem.
.

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