A lamina has the shape of a portion of a sphere ? + y? + z2 = a? that lies within cone x = z2 + y?. Let S be the spherical shell centered at the origin with radius a, and let C be the right circular cone with a vertex at the origin and an axis of symmetry that coincides with the x-axis. Determine the mass of the lamina if the density is given by 8 (x, y, z) = x?y?z. y