8. A homogeneous solid of constant density p is bounded by the cone z = x + y and the paraboloid z = x + y. Find (a) its center of mass, (b) its moment of inertia with respect to the z-axis. Use your TI-89 to evaluate the integrals for both parts. 9. A solid is bounded by the cone z = x + y and the plane z = 5, given that the mass density at P (x,y,z) is directly proportional to the distance from the z-axis to P. Find its mass. Show your work. 10. Show that for a right triangle the average distance from any point in the triangle to one of the legs is one-third the length of the other leg. Y a Note: For all problems, show your inequalities, integral set-ups, and the projection in the xy-plane.