just saw this message from rwg several weeks back (june 22, to be precise):

with a nice shortcut and an interesting answer: Q: A cylindrical water tank, radius 1, rests on its side, skewered by a coaxial bar of radius r. Choose r to maximize capacity if the water level may not exceed the top of the bar.

A: .retal etaitnereffid od gniog tsuj er'uoy ecnis )2^x-1(trqs largetni rotces eht od ot deen t'nod uoy taht si tuctrohs ehT .)2^ip+1(trqS/1

or do it geometrically ... the maximum occurs when the circumference of (the cross section of) the bar equals the length of the chord formed by the cross section of the top of the water. mike