1. The problem statement, all variables and given/known data Find the center of mass of a hemisphere of radius R. 2. Relevant equations R_cm = (rho/M) Integral[ (vector r) dv] dv = r^2 Sin[theta] dr d[theta] d[phi] 3. The attempt at a solution In spherical polar coordinates, vector r = r r-hat, so the argument of the integral should be: r^3 Sin[theta] dr d[theta] d[phi] Well, that's what I would expect... I keep ending up with 3R/4, but other sources have it as 3R/8, and I see that the volume element dv is written with an extra Cos[theta] which I do not understand.......... I have no problem integrating over volumes in E&M problems, so I do not get why this is such an issue for me.