I'm way out of practice with this stuff, but for fun tried a different approach. I figured, apply a scale factor (f) to the height and radius of a cone, to make the volume half what it was.

V1 = (0.333...).Pi.r^{2}.h

V2 = (0.333...).Pi.(f.r)^{2}.(f.h) = 0.5 V1

f^{3}.(0.333...).Pi.r^{2}.h = 0.5 (0.333...).Pi.r^{2}.h

f^{3} = 0.5

f = 0.793701

Which would place x, 0.206 from the base of the cone. That's "close" to the "one quarter" on that Wiki page, but not *very* close. (But does match your number).

(Googling, it seems the answer involves integration...)

Last edited by pzkpfw; 2012-Mar-15 at 12:07 AM.
Reason: Add last brackets, then more

Thank you, members of cosmoquest forum, you are a part of my life I value.