Solid of revolution

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, engineering, and manufacturing, a solid of revolution is a solid figure obtained by rotating a plane curve around some straight line (the axis) that lies on the same plane. Assuming that the curve does not cross the axis, the solid's volume is equal to the length of the circle described by the figure's centroid, times the figure's area (Pappus's second centroid Theorem). Rotating a curve A representative disk is a three-dimensional volume element of a solid of revolution. The element is created by rotating a line segment (of length w) around some axis (located r units away), so that a cylindrical volume of ¿¿r2w units is enclosed.