Explanation:
Cylinder (geometry)
A right circular cylinder
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.
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). If the
cylinder has a radius r and length (height) h, then its volume is given by
V = πr^{2}h
and its surface area is:
§ the
area of the top (πr^{2}) +
§ the
area of the bottom (πr^{2}) +
§ the
area of the side (2πrh).
Therefore without the top or bottom (lateral area), the surface
area is:
A = 2πrh. (Our solved example in
mathguru.com uses this concept)
With the top and bottom, the surface area is:
A = 2πr^{2} + 2πrh = 2πr(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, i.e. the cylinder fits
in a cube (height = diameter)
http://en.wikipedia.org/wiki/Cylinder_(geometry)
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above explanation is copied from Wikipedia, the free encyclopedia and is
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License.