1. The problem statement, all variables and given/known data Problem (also attached as TheProblem.jpg): Find the center of mass of the surface of the sphere x^2 + y^2 + z^2 = a^2 contained within the cone z tanγ = sqrt(x^2 + y^2), 0 < γ < π/2 a constant, if the density is proportional to the distance from the z axis. Hint: R_cm = ∫∫_S δR dS / ∫∫_S δ dS, where δ is the density. Solution: The solution is attached as TheSolution.jpg. 2. Relevant equations Spherical coordinates: x = p sinϕ cosθ, y = p sinϕ sinθ, z = pcosθ ∫∫_E∫ f(x,y,z) dV = ∫∫_E∫ f(p sinϕ cosθ, p sinϕ sinθ, p cosθ) p^2 sinϕ dp dθ dϕ 3. The attempt at a solution The first thing I'm stuck on is knowing what δ and dS are. How do I determine what those are (without “cheating” and looking at the solution)? Any input would be greatly appreciated!