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In elementary work, a cylinder, if taken, say, with its axis vertical, would be reckoned to consist of a circular base, a circular top of the same size, and the curved surface formed by the vertical line segments joining them. For a cylinder with base of radius r and height h, the volume equals πr2h, and the area of the curved surface equals 2πrh.In more advanced work, a cylinder is a surface, consisting of the points of the lines, called generators, drawn through the points of a fixed curve and parallel to a fixed line, the generators being extended indefinitely in both directions. Then a right-circular cylinder is one in which the fixed curve is a circle and the fixed line is perpendicular to the plane of the circle. The axis of a right-circular cylinder is the line through the centre of the circle and perpendicular to the plane of the circle, that is, parallel to the generators.

Subjects: Mathematics.

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