Cylinders Cylinders A cylinder is one of the most basic curvilinear geometric shapes, the surface formed by the points at a fixed distance from a given line segment, the axis of the cylinder. The solid enclosed by this surface and by two planes perpendicular to the axis is also called a cylinder. The surface area and the volume of a cylinder have been known since deep antiquity. In differential geometry, a cylinder is defined more broadly as any ruled surface spanned by a one-parameter family of parallel lines. A cylinder whose cross section is an ellipse, parabola, or hyperbola is called an elliptic cylinder, parabolic cylinder, or hyperbolic cylinder respectively. The open cylinder is topologically equivalent to both the open annulus and the punctured plane.
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Common use :- In common use a cylinder is taken to mean a finite section of a right circular cylinder, i.e., the cylinder with the generating lines perpendicular to the bases, with its ends closed to form two circular surfaces, as in the figure (right). Volume :- Having a right circular cylinder with a height h units and a base of radius r units with the coordinate axes chosen so that the origin is at the center of one base and the height is measured along the positive x-axis. Cylindric section :- Cylindric sections are the intersections of cylinders with planes. For a right circular cylinder, there are four possibilities. A plane tangent to the cylinder, meets the cylinder in a single straight line. Moved while parallel to itself, the plane either does not intersect the cylinder or intersects it in two parallel lines. All other planes intersect the cylinder in an ellipse or, when they are perpendicular to the axis of the cylinder, in a circle. As we know that the volume of cylinder = ⊼r2h, And surface area of cylinder = 2⊼r(r + h), We know that the value of ⊼ = 3.14, Given, radius = 6, Height = 4, On putting the value we get, Volume of right circular cylinder = ⊼r2h, V = 3.14 * (6)2 * 4,
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V = 3.14 * 36 * 4, V = 3.14 * 144, V = 452.16 inch3, Surface area of right circular cylinder = 2⊼r (r + h), SA = 2⊼r (r + h), = 2 * 3.14 * 6 (6 + 4), = 2 * 3.14 * 6 (10), = 2 * 3.14 * 60, = 376.8 inch2. This is all about Cylinders.
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