Second Guldin Theorem The volume of a solid generated by the revolution of a plane region about an axis lying in the plane of this region and not cutting the region is equal to the product of the area of the region and the length of the path described by the mass center of the region. This is the second theorem of Guldin (1577-1643).
(a) Use the Guldin theorem to determine the mass center of the semicircle area of Figure 2.55(a).
(b) Use the result of part (a) to determine the volume of the solid object that is made by the revolution of the semicircle area of Figure 2.55(b) about the Y -axis.
