Hey guys, this is my first thread here. I'm just looking for a hint or two (no answer please). A sphere of styrofoam has radius R. A cavity of radius R/2 centered a distance R/2 directly above the center of the sphere is hollowed out and filled with a solid material of density five times the density of styrofoam. Where is the center of mass of the new sphere? I figured that to do three dimensional center of mass calculations, I just break it down for each dimension and solve, so I was able to get the center of mass for the pre-cavity styrofoam sphere, which is just R. I think that, if the new sphere's center of mass were to be calculated in the same manner, the mass density would no longer be constant and would therefore be a function. However, that function is eluding me.