Cylinder (geometry) Totally Explained

Everything about Cylindrical totally explained

A cylinder is one of the most basic curvilinear geometric shapes: the surface formed by the points at a fixed distance from a given straight line, 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. The most common type of such generalized cylinders is given by certain quadric surfaces. A cylinder whose cross section is an ellipse, parabola, or hyperbola is called an elliptic cylinder, parabolic cylinder, or hyperbolic cylinder.

Common usage

In common usage, a cylinder ' is taken to mean a finite section of a right circular cylinder with its ends closed to form two circular surfaces, as in the figure (right). If the cylinder has a radius r and length (height) h, then its volume is given by ť $V = pi r^2 h ,$

and its surface area is:

Area of the top is $pi r^2$
Area of the bottom is $pi r^2$
Area of the side is $2 pi r h$

Therefore without the top or bottom (lateral area), the surface area is ť

A = 2 pi r h.

With the top and bottom, the surface area is ť

A = 2 pi r^2 + 2 pi r h = 2 pi r (r + h ).,

For a given volume, the cylinder with the smallest surface area has h = 2r. For a given surface area, the cylinder with the largest volume has h = 2r, for example the cylinder fits in a cube (height = diameter.)

Other types of cylinders

An elliptic cylinder is a quadric surface, with the following equation in Cartesian coordinates:
ť

left(frac
ight)^2 = 1

and the parabolic cylinder:
ť

x^2 + 2ay = 0. ,

Trivia

The volume of the cylinder is 3 times the volume of a cone with equal radius.Further Information

Get more info on 'Cylindrical'.

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