A solid is bounded below by the cone z = √ =√x² + y² and above by the plane z = 1. Find the center of mass and the moment of inertia about the z-axis if the density is 8(r,0,z) = 4z. The center of mass is (x,y,z) = C

2. Calculate the Jacobian of the coordinate change (x, y, z) to cylindrical coordinates (r, 0, z).

Find the center of mass of a solid of constant density bounded below by the paraboloid z = x² + y² and above by the plane z = 100. Then find the plane z = c that divides the solid into two parts of equal volume. This plane does not pass through the center of mass.

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