1. The problem statement, all variables and given/known data The distribution of mass on the hemispherical shell: z=(R2-x2-y2)1/2 is given by σ(x,y,z)=(σ0/R2)(x2+y2) where σ0 is a constant. Find the moment of inertia about the z-axis of the hemispherical shell. 2. Relevant equations I=∫r2dm 3. The attempt at a solution r2 is just R2. ∫dm in spherical coordinates is: σ0R2∫∫sin3θ dθ d(phi) with boundaries 0 to pi/2 for θ, and 0 to 2pi for phi. The completed definite integral representing the total mass is then: (4pi/3) σ0R2. I feel pretty confident about that, since it is given in the back of the book as the first step in the problem. What I don't understand is why the moment of inertia is anything more than just this value times another R2 to give: (4pi/3) σ0R4. The answer is supposed to be: (16pi/15) σ0R4. So, I'm guessing there's something more to the calculation of moment of inertia. I've been looking through the different derivations of moments but can't see how to get the right factor. I could use a hint.