(Solution) - a The base of a solid is a square with -(2025 Original AI-Free Solution)

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(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.