| 翻訳と辞書 |
| solid of revolution ： ウィキペディア英語版 |
solid of revolution
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 multiplied by the figure's area (Pappus's second centroid Theorem).
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 units is enclosed.
==Finding the volume==
Two common methods for finding the volume of a solid of revolution are the disc method and the shell method of integration. To apply these methods, it is easiest to draw the graph in question; identify the area that is to be revolved about the axis of revolution; determine the volume of either a disc-shaped slice of the solid, with thickness ''δx'', or a cylindrical shell of width ''δx''; and then find the limiting sum of these volumes as ''δx'' approaches 0, a value which may be found by evaluating a suitable integral.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
■ウィキペディアで「solid of revolution」の詳細全文を読む
スポンサード リンク
| 翻訳と辞書 : 翻訳のためのインターネットリソース |
Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.
|
|