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  $(0,0,\frac{1}{2})$?

Use $z_0=\displaystyle {{\int z ds}\over {\int ds}}$ where $z=\cos\phi$ and $ds=\sin\phi d\theta d\phi$. That gives your 1/2.
