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.

Najabhai

Let F = (z, xy, x² + y²). Compute the work done by the force when moving a particle located at the point (3, 1, 1), counter-clockwise, when viewed from above, along a circular path of radius 3 in the plane z = 1, centered at the point (0, 1, 1).

A solid is bounded below by the cone z = Vx +y 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) = 3z. %3D The center of mass is (x,y,z) = ( (Type integers or simplified fractions.)

I have gotten the first two coordinates right, but I can figure out the z coordinate