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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク spherical cap ： ウィキペディア英語版 spherical cap In geometry, a spherical cap or spherical dome is a portion of a sphere cut off by a plane. If the plane passes through the center of the sphere, so that the height of the cap is equal to the radius of the sphere, the spherical cap is called a ''hemisphere''. == Volume and surface area == If the radius of the base of the cap is $a$, and the height of the cap is $h$, then the volume of the spherical cap is〔.〕 :$V\; =\; \backslash frac\; (3a^2\; +\; h^2)$ and the curved surface area of the spherical cap is〔 :$A\; =\; 2\; \backslash pi\; r\; h$ or :$A=2\; \backslash pi\; r^2\; (1-\backslash cos\; \backslash theta)$ The relationship between $h$ and $r$ is irrelevant as long as 0 ≤ $h$ ≤ $2r$. The red section of the illustration is also a spherical cap. The parameters $a$, $h$ and $r$ are not independent: :$r^2\; =\; (r-h)^2\; +\; a^2\; =\; r^2\; +h^2\; -2rh\; +a^2$, :$r\; =\; \backslash frac$. Substituting this into the area formula gives: :$A\; =\; 2\; \backslash pi\; \backslash frac\; h\; =\; \backslash pi\; (a^2\; +\; h^2)$. Note also that in the upper hemisphere of the diagram, $\backslash scriptstyle\; h\; =\; r\; -\; \backslash sqrt$, and in the lower hemisphere $\backslash scriptstyle\; h\; =\; r\; +\; \backslash sqrt$; hence in either hemisphere $\backslash scriptstyle\; a\; =\; \backslash sqrt$ and so an alternative expression for the volume is :$V\; =\; \backslash frac\; (3r-h)$. 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「spherical cap」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.