Set up the double integral in polar coordinates that

Question

1. Set up the double integral in polar coordinates that calculates the volume of the given solid. Do not evaluate the integral.

Below the paraboloid z = 8 - 2x² - 2y² and above the xy-plane.

2. A lamina occupies the part of the disk x² + y² 49 in the first quadrant. Set up the integrals that calculate the center of mass of the lamina if the density at any point is proportional to the square of its distance from the origin. Do not evaluate the integrals.