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.r2.h
V2 = (0.333...).Pi.(f.r)2.(f.h) = 0.5 V1
f3.(0.333...).Pi.r2.h = 0.5 (0.333...).Pi.r2.h
f3 = 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
Get up, a get-get, get down.