What is the centroid of a hollow spherical cap? I have a unit hollow sphere which I cut along a diameter to generate two equivalent hollow hemispheres.  I place one of these hemispheres on an (x,y) plane, letting it rest on the circular planar face where the cut occurred. 
If the hemisphere was solid, we could write that its centroid in the above case would be given as $(0,0,\frac{3}{8})$.  Given that the hemisphere is hollow, can we now write its centroid as  $(0,0,\frac{1}{2})$?

A simpler argument appeals to the hat-box theorem (http://mathworld.wolfram.com/ArchimedesHat-BoxTheorem.html).
By symmetry the centroid of the hemispherical cap lies on the $z$-axis; all that remains is to find its $z$-coordinate. But by the hat-box theorem, that's the same as the $z$-coordinate of the centroid of the cylinder of radius 1 and height 1 resting on the $x,y$ plane, which by symmetry is 1/2.
(Maybe this is what horchler and user86742 had in mind?)
