(a) The base of a solid is a square with vertices located at (1, 0), (0, 1) (– 1, 0) and (0, – 1). Each cross-section perpendicular to the -axis is a semicircle. Find the volume of the solid.
(b) Show that by cutting the solid of part (a), we can rearrange it to form a cone. Thus compute its volume more simply.