How to calculate the volume of the cylinder?

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How to calculate the volume of the cylinder?

In the world, quite a lot of objects have a cylindrical shape, the volume of which periodically must be calculated. This can be a culinary task, and can be useful in construction. In this case, the scope of use is not so important, and the method of calculation is important. In mathematics, describing various objects and phenomena of our life, such means are theorems and formulas.

Algorithm for determining the volume of the cylinder

Let us return to the method of calculating the volume of a cylinder, if its height and radius are known. To begin, you will need to answer a series of uncomplicated questions First you need to determine which cylinder is in front of you.

A classic ideal variant is often considered when a cylinder is obtained by rotating a rectangle around one of its sides, and then the bases are circles whose radii are equal to each other, and the height will be generatrix. Such a cylinder is called a round straight.

The second task in determining the volume of the cylinder is to find the height. Take advantage of the rule will be easier.It is enough to connect the centers of the circles among themselves.

How to calculate the volume of a round straight cylinder

The volume of a circular straight cylinder is the product of the area of ​​the circle lying at the base of the cylinder by the height and is expressed by the following formula:

V = P * R2* Где, where:cylinder

  • V is the volume of the cylinder;
  • Π = 3, 14 and is a constant value;
  • R is the radius;
  • H - height.

Example. It is required to calculate the volume of the cylinder, if it is known that its height is perpendicular to the base and is 6 cm, and the radius is 2 cm.

Solution: V = 3.14 * 6 * 2 * 2 = 75.36 cm3.

How to calculate the volume of a truncated round cylinder

The situation changes if we are dealing with a truncated round cylinder. A distinctive feature of this type of cylinder from the classical one may be that its bases do not lie on parallel planes, and therefore the formula for calculating the volume of a cylinder takes on a slightly different look:

V = P * R2* (H1+ H2) / 2, where:cylinder

  • V is the volume of the cylinder;
  • R is the radius;
  • H1 - high altitude;
  • H2 is a smaller height.

Example 2. It is required to calculate the volume of a truncated round cylinder, if it is known that the cylinder radius is 3 cm, the greater height is 5 cm, and the smaller one is 3 cm.

Solution: V = 3.14 * 3 * 3 * (5 + 3) / 2 = 113.04 cm3.

The heights are numbered arbitrarily, so that for solving a specific task, the order can be chosen by the participant himself.As is known, the sum does not change from the rearrangement of places.

There are other types of cylinders, for example: elliptic, parabolic and hyperbolic. They are described by second-order equations, and completely different parameters are needed to calculate their volume.