How to find the volume of a cylinder?

The word "cylinder" came to us from the Greek language - "κύλινδρος" - in Russian it means "roller" or "skating rink", but has three meanings that are related to these two concepts.

The first is a geometric body that is formed by rotating around one of the sides of a rectangle. The second is used in the art to refer to a device or part, for example, "cylinder piston" or "engine cylinder". The third is a man's headpiece, which has a corresponding shape.

The question "how to determine the volume of a cylinder?" Makes sense for the first two values when solving geometric problems. It is relevant in educational, scientific or technical (design, installation, construction, repair, etc.) process, as well as in everyday life. For the third case, it is appropriate to talk about the linear dimensions of the headgear, which determine its style and size.

The answer to the question "how to find the volume of a cylinder?" Will depend on the form of this geometric body. Cylinders are inclined or straight, as well as circular, elliptical, hyperbolic, parabolic.

More often this word is understood as a straight circular body. It can be represented in the form of a space that is bounded by two parallel planes of equal size and shape in the form of a circle and a lateral surface in the form of a rectangle (in expanded form), the two opposite sides of which coincide with the line delineating the circle of these parallel surfaces. In this case, the lateral surface is perpendicular to it. All the further arguments in this article will relate to a direct circular cylinder, since the description of any other kind can be a separate topic.

To understand how to calculate the volume of a cylinder, the interpretation of the word "volume" will also help. It is used as a quantitative characteristic of the space that a substance or body occupies. It has a close connection with the concept of "capacity", that is, with the ability, determined by linear dimensions and shape, to contain in the vessel or capacity a certain amount of something. The volume of the cylinder is a special case of the concept of "body volume". It can be in the form of a sphere, a cube, any polyhedron, a cone, and so on.

The cylinder capacity is applicable for a railway tanker in which 38 m3 (35 tons) of a chemical such as styrene or 73 m3 (55 tons) of Super Euro-98 gasoline can be transported. For internal combustion engines, the most important design parameter is the working volume. It determines its power and other characteristics: for subcompacts it can be up to 1.1 liters, for large cars it can exceed 3.5 liters.

So after all, how to find the volume of a cylinder? This figure, like that of any other body, is considered multiplying the area by its height, provided that the size and shape of its cross-sectional area at any point in height are the same.

For example, for a body in the shape of a cone or a ball, this technique does not work. The formula for calculating the volume of a straight circular cylinder can be written as the product of the number π (the mathematical constant is 3.14) by the square of the radius (r is equal to half the diameter) of the circle lying at the base of the cylinder and the height of the cylinder (h): V = π • R2 • h.

Values such as radius and height should be expressed by one measurement unit (if height in meters, then the radius should be expressed in meters): mm, cm, dm, m, km. Then, the volume is obtained in mm3, cm3, dm3 (l), m3, km3, respectively. As an example, the basic and derived units of measure relating to the SI system were given .

Are used, but much less often, and other off-system units of measure, such as pint, quart, gallon, barrel and others. The problem: how to find the volume of the cylinder, the height of 5 m and the radius of the base 2 m? The answer is: V = 3.14 • 2 • 2 • 5 = 62.8 m3.

From the examples given, it becomes obvious that the problems formulated in the form of a question, "How to find the volume of a cylinder?" Are of great practical importance. With the decision of their meet in the practical work experts and engineers of various specialties. Gas workers and oil producers have to calculate the amount of gas, oil or other petroleum products pumped through pipelines. This determines the volume of the cylinder, whose height is equal to the length of the pipeline with a known internal diameter.

Oil refiners and petrochemists calculate the volume of the product (gas or liquid) filling the reservoir of a cylindrical shape, knowing the geometric dimensions of this capacitive apparatus and the height of the liquid poured in it. The same applies to any product (food, refining or petrochemicals) that is poured into drums, glass bottles or other cylindrical containers.

Any hostess who cooks food can calculate the volume of a product poured or poured into a cylindrical vessel, for this it is sufficient to know its diameter and fill height of this container.