Cylinder

A cylinder is a three-dimensional shape consisting of two parallel, congruent circular bases connected by a curved surface. It is one of the most common geometric forms, alongside the sphere and cone.

When the line connecting the two bases is perpendicular to the planes of the bases, the shape is called a right circular cylinder. If this line is at an angle, it is called an oblique cylinder.

Geometric definition

In general, a cylinder can be generated by moving a straight line along a closed planar curve while keeping the line parallel to itself. When the curve is a circle, the result is the common circular cylinder. A right circular cylinder can also be defined as the solid formed by rotating a rectangle about one of its sides.

Measurements

If r is the radius of the base and h is the height, the volume of a right circular cylinder is V = πr²h, which equals the area of the base (πr²) multiplied by the height. The lateral surface area is 2πrh, while the total surface area is 2πrh + 2πr². The volume formula V = πr²h also applies to oblique cylinders, where h is taken as the perpendicular distance between the two bases.

Other types

The term cylinder is also used for non-circular shapes: for example, an elliptic cylinder, which has an ellipse as its base. In higher mathematics, the term 'cylinder' refers only to the curved surface, with the bases excluded.

Applications

The cylindrical shape is widely used in engineering and everyday life: in engine cylinders, pipes, tubes, gas canisters, and storage containers. This is because the shape distributes stress evenly and is simple to manufacture.