What is the center of gravity of the solid formed when the plane region bounded by y = x, y = 2x, and x + y = 6 is revolved about the y-axis ? O (13/5,0) O (3/5,0) 2 O (0, 13/5) O (0,3/5) O NA

Evaluate ||| Vx² + y² + 2²¢V where S lies above the cone z = = /x² + y° and S between the spheres x +y +z² =1 and x + y +z' = 4.

Evaluate 5z dV , where E is E the region bounded below by the Vx2 + y? and above by the sphere x2 + y² + z² = 1, using cone z = a change of variables of your choice. Select one: O a. (8 – V2) 12 O b. -(8 – V3) 12 O c. (4 – V2) - 18 O d. " (4 – V3) 6. O e. " (4 – v2) 6.

2 A circular wire hoop of constant density 8=3 lies along the circle x² + y² = 7a² in the xy-plane. Find the hoop's moment of inertia, I2, about the z-axis. The hoop's moment of inertia about the z-axis is l₂ = (Type an exact answer, using it as needed.)