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shell of revolution - translation to russian
![[[Mathematics and art]]: study of a vase as a solid of revolution by [[Paolo Uccello]]. 15th century](https://commons.wikimedia.org/wiki/Special:FilePath/Paolo uccello, studio di vaso in prospettiva 02.jpg?width=200 "[[Mathematics and art]]: study of a vase as a solid of revolution by [[Paolo Uccello]]. 15th century")
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Definition
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Wikipedia
In geometry, a solid of revolution is a solid figure obtained by rotating a plane figure around some straight line (the axis of revolution) that lies on the same plane. The surface created by this revolution and which bounds the solid is the surface of revolution.
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 multiplied by the figure's area (Pappus's second centroid theorem).
A representative disc 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 πr2w units is enclosed.
