## Center of mass of a half-ball

Hi, I've been working on the following question for a little while. I've looked it over several times and I can't find any obvious (to me anyway) errors in my work. Would you please scan it through and let me know if I am correct or, if not, please guide me in the right direction so I can try again.

I have attached a scanned copy of the question and my work.

 Recognitions: Gold Member Science Advisor Staff Emeritus I don't see anything wrong with it. (Except that you really don't need to integrate to find the volume of the hemisphere: it is (1/2)(4$\pi$)!)