Cylinder (geometry)

A finite cylinder (from the ancient Greek. Κυλίνδειν kylíndein, roll ',' roll ') is, according to the general definition of two parallel, flat, congruent surfaces ( base and top surface ) and a casing or cylinder surface finite body, the lateral surface is formed by parallel lines. That is, the cylinder is formed by displacement of a flat surface or a curve along a straight line that is not in this plane. The height of the cylinder is given by the distance between the two planes in which the base and top surface are.

Are the lines perpendicular to the base and top surface, it is called a straight cylinder. If the geometry of a cylinder is mentioned, it often is a ( straight ) circular cylinders, as described further below.

Properties

Volume, surface and surface of a general cylinder are calculated as follows:

Volume:

Lateral surface:

Surface:

G stands for the contents of the base, U for the scope of the base area or the length of the trajectory; h denotes the height of the cylinder.

Straight cylinder with an elliptical base

Straight generalized cylinder

Slate general cylinder

Circular cylinder

A circular cylinder formed by the displacement of a circle parallel to a straight line through the center of the circle, the axis of which does not lie in the plane of the circle. A circular cylinder defined by two parallel circular surfaces ( base and top surface ) and the so-called outer surface.

Variants

One of the distinctions between the right circular cylinder or rotary cylinder whose axis is perpendicular to the circular plane, and the oblique circular cylinder in which this is not the case. The cross-section perpendicular to the axis has the shape of an ellipse.

A rotating cylinder with h = 2r is called equilateral cylinders. This designation is explained as follows: If you cut such a cylinder with a plane containing the axis, we obtain a square.

Does the circular cylinder, a bore along its axis, then one speaks of a hollow cylinder.

An object whose height (thickness) is very small in proportion to its diameter, Ronde is called. Traffic signs with a ban ( characters 250-267 ) are ronde shaped in Germany.

Properties

The volume of a ( straight or crooked ) circular cylinder is calculated from the base surface of radius r and height h:

The lateral surface of a right circular cylinder is calculated from:

For the surface of a straight circular cylinder is obtained:

The summand of the lateral surface in this formula arises from the fact that these to a rectangle with sides of length ( circumference ) and (height) is unwound.

Hollow cylinder

For a hollow cylinder - approximately a straight piece of pipe - are the determining variables in addition to the height of the outer and the inner radius respectively. The wall thickness is thus. The corresponding lateral surfaces are calculated as follows or. The total surface is given by

While the volume of the hollow cylinder

Amounts.

Volume calculation of a horizontal circular cylinder (tank problem)

The calculation of the contents of a partially filled lying circular cylinder can be made based on the length of the radius and the filling level. According to the above equation Volume = base · height, the volume of the charge results by multiplying the surface area of the circular segment with the length of the cylinder: