The homogeneous circular cylinder shown has a mass m, and the diameter OB of its top surface forms 45° angles with the x and z axes.

(a) Determine the principal mass moments of inertia of the cylinder at the origin O.

(b) Compute the angles that the principal axes of inertia at O form with the coordinate axes.

(c) Sketch the cylinder, and show the orientation of the principal axes of inertia relative to the x, y, and z axes.