Question: Let the surface S be the upper hemisphere of the sphere x² + y² + z² = a² (i.e., the part of the sphere in the region \(z\ge 0\) ). Find \(\bar{z}\) the z-coordinate of the centroid of S and the moment of inertia of S for rotation about the z-axis. These are surface integrals, don’t do the triple integral over a solid region.