1. The problem statement, all variables and given/known data Evaluate triple integral z^2 dxdydz throughout i) the part of the sphere x^2 + y^2 + z^2 = a^2 (first octant) ii)the complete interior of the sphere x^2 + y^2 + z^2 = a^2 (first octant) 2. Relevant equations It is probably good idea to work in spherical coords. z = r*cosφ x = r*sinφ cosθ y = r*sinφ sinθ dxdydz = r^2 sinφ drdφdθ 3. The attempt at a solution I'l start at part ii) because its the part I can do. Here the boundaries are: 0 =< r < a 0 =< φ < pi/2 0 =< θ < pi/2 the integration now becomes: (Int[r=0, a] r^4 dr )( Int[φ=0, pi/2] sinφcos^2 φ)( Int [θ=0, pi/2]) = r^5/30 * pi i) But for part i), I am confused. The integral should be evaluated only on the surface of the sphere. The radius a is constant in length, so how should r be defined? a < r < a, makes no sense. Need advice.