5. Let be the solid region that is inside the sphere 2 + 2 + 2 = 2, on the left of the cone = 2 + 2, on the right of the XZ-plane and in the first octant. Let the density of the solid at (, , ) be (, , ) = 2 + 2. (a). Sketch the solid region . (b). Describe (using the set builder notation), then set up, but DO NOT evaluate, iterated integral(s) for the mass of using the rectangular coordinates. (c). Repeat (b) using the cylindrical coordinates. (d). Repeat (b) using the spherical coordinates.

Let E be the solid region that is inside the sphere x2 + yz + z2 = 2, on the left of the coney = vx2 + z2, on the right of the XZ-plane and in the first octant. Let the density of the solid at (x, y, z) be p(x, y, z) = Vx2 + z2. (a). Sketch the solid region E. (6 points) (b). Describe E (using the set builder notation), then set up, but DO NOT evaluate, iterated integral(s) for the mass of E using the rectangular coordinates. (12 points) (c). Repeat (b) using the cylindrical coordinates. (10 points) (d). Repeat (b) using the spherical coordinates. (6 points)