Alright following the my notes so far which had a sort of similar but different question, I guess that the height is z+R? Assuming if this is right, the limits of integration will be [0,R]x[-Pi/2,-0]x[0,2*Pi] (since we are looking at the lower hemisphere).

However, if I try to calculate the first moments, I get this horrible expression which I can't integrate. Maybe this indicates that I am moving in the wrong direction?