1. The problem statement, all variables and given/known data Here is my assignment, http://imgur.com/1edJ3g5 I figured it would be easier if we know we are both looking at the same thing! I'm looking for help with question 2. I seem to be having trouble with the integration. 2. Relevant equations r=acosθ x^2 + y^2 + z^2 = a^2 Cylindrical Coordinates ~ x^2 + y^2 = r^2 3. The attempt at a solution So far I found my bounds of integration to be, -sqrt( a^2 - r^2 ) ≤ z ≤ sqrt( a^2 - r^2 ) 0 ≤ r ≤ acosθ -pi/2 ≤ θ ≤ pi/2 After doing this I came up with the integral, ∫∫∫ r dzdrdθ Since I converted to cylindrical coordinates I need to add the "r" to my integral correct? From here I integrated and subbed in my limits and found ∫∫2*r*sqrt(a^2 - r^2) drdθ After doing this if I integrate again I get a really messy answer which I don't think I could integrate again for dθ. Have I messed up somewhere? If I changed the order of my integral would that help at all?