Cylinder - Enchu

Japanese: 円柱 - えんちゅう

Given a plane α, a circle c on it, and a line l that intersects with α, the surface formed by all the lines that pass through any point on the circumference of c and are parallel to l is called a cylindrical surface (oblique cylindrical surface), and these lines are called generatrix. When this cylindrical surface is cut by a plane β that is parallel to α, the solid surrounded by the two planes α and β and the cylindrical surface is called a cylinder (oblique cylinder) ( Figure (1)). The circle c is called the base of the cylinder, and the distance between the two planes is called the height. The volume of a cylinder with a base radius r and height h is V = π r ² h . In the cylinder shown previously, when the plane α and the line l are perpendicular, this cylinder is called a right circular cylinder ( Figure (2)). A right circular cylinder can also be said to be a solid formed by rotating a rectangle around one side of the rectangle. The axis of rotation in this case is called the axis of the right circular cylinder. The area of the side of a right circular cylinder with a base radius r and height h is S = 2π rh .

[Minoru Kurita]

Cylinder (Diagram)
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Cylinder (Diagram)

Source: Shogakukan Encyclopedia Nipponica About Encyclopedia Nipponica Information | Legend

Japanese:

平面αとその上の円c、およびαと交わる直線lが与えられているとき、cの周上の任意の点を通ってlに平行な直線の全体でできる面を円柱面（斜円柱面）、これらの直線を母線(ぼせん)という。この円柱面をαに平行な平面βで切るとき、2平面のα、βと円柱面で囲まれた立体を円柱（斜円柱）という（図の(1)）。円cを円柱の底面といい、2平面の距離を高さという。底面の半径r、高さhの円柱の体積はV＝πr²hである。前に示した円柱で、平面αと直線lが垂直のとき、この円柱を直円柱という（図の(2)）。直円柱は、長方形をその1辺を軸として回転してできる立体ともいえる。このときの回転軸を直円柱の軸という。なお底面の半径がr、高さhの直円柱の側面の面積はS＝2πrhである。