Cylinder
In its simplest form, a cylinder (from Greek κύλινδρος – kulindros, "roller, tumbler") is the surface formed by the points at a fixed distance from a given straight line called the axis of the cylinder. It is one of the most basic curvilinear geometric shapes.
Commonly the word cylinder is understood to refer to a finite section of a right circular cylinder having a finite height with circular ends perpendicular to the axis as shown in the figure. If the ends are open, it is called an open cylinder. If the ends are closed by flat surfaces it is called a solid cylinder. The formulae for the surface area and the volume of such a cylinder have been known since deep antiquity.
If the cylinder has a radius r and length (height) h, then its volume is given by
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. A plane section at a distance of x units from the origin has an area of A(x) square units where
or
An element of volume, is a right cylinder of base area Awi square units and a thickness of Δix units. Thus if V cubic units is the volume of the right circular cylinder, by Riemann sums,
Using cylindrical coordinates, the volume can be calculated by integration over
Still using a radius r and length (height) h, the surface area of a cylinder is made up of three parts:
The area of the top and bottom is always the same, and is also called the base area, B. The area of the side is also known as the lateral area, L.
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