In wikipedia and elsewhere it is stated that: The center of mass of a conic solid of uniform density lies one-quarter of the way from the center of the base to the vertex, on the straight line joining the two.

But when I set up the problem as shown in this image, with "x" being the location of the center of mass then I get:

x = h*(1 - 1/(2)^{1/3}) = 0.2063*h

I essentially set the volume (it is uniform density) of the small cone, V2 = V3, the mass of the frustum, then solve for "x"

Known: V3 = V1 - V2

I used centroids and areas to create a solid/volume of revolution: http://en.wikipedia.org/wiki/Pappus's_centroid_theorem

What am I missing or is wikipedia wrong?