Cylindrar

Cylindrar is the Swedish plural form of cylinder. In geometry, a cylinder is a three‑dimensional shape formed by translating a straight line (the generatrix) along a fixed direction so that every point on the line remains at a constant distance from a fixed line, called the axis. If cross‑sections by planes perpendicular to the axis are circles, the shape is a circular cylinder; if the cross‑sections are ellipses, it is an elliptic cylinder. The axis may be perpendicular to the base plane (right cylinder) or inclined (oblique cylinder).

Common types include right circular cylinders,Elliptic cylinders, and oblique cylinders. A right circular cylinder has circular bases and an axis perpendicular to those bases, resulting in uniform cross‑sections along its length. An elliptic cylinder has elliptical cross‑sections when cut perpendicular to the axis. An oblique cylinder has its axis at an angle to the base, causing the side surface to slant.

Key formulas for a circular cylinder with base radius r and height h (the length along the axis) are:

- Volume V = π r^2 h

- Total surface area A = 2π r^2 + 2π r h

- Lateral surface area (excluding bases) L = 2π r h

In Cartesian coordinates, a right circular cylinder along the z‑axis is described by x^2 + y^2 = r^2, independent of z, with z ranging over the cylinder’s height. Elliptic cylinders satisfy x^2/a^2 + y^2/b^2 = 1, again independent of z.

Applications of cylindrar range across engineering and everyday objects, including pipes, tubes, cans, columns, and mechanical pistons. They provide simple, well‑defined cross‑sections and volume properties that underpin manufacturing, construction, and design.