At the solution of mathematical and technical tasks sometimes it is required to learn cylinder volume. The similar task often arises also in life as many tanks (barrels, buckets, banks, etc.) have the cylindrical form. Of course, if the radius and height (length) of a cylinder are known, it is very easy to calculate its volume. However in practice these parameters are not always set and cylinders are not only straight lines circular.
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1. To learn cylinder volume, increase its height by number "пи" and by a radius square. In the form of a formula this rule looks as follows: About = In * π * P², where About - cylinder volume, In – cylinder height, P – cylinder basis radius, π – number "пи", approximately equal 3.14. The volume of a cylinder will be measured in the cubic units of measure corresponding to the radius and height. I.e. if, for example, the radius and height of a cylinder are set in meters, its volume will turn out in cubic meters (m³). The aforesaid ruled fairly only for a "usual", i.e. direct circular cylinder (a cylinder which basis represents a circle, and the guide is perpendicular to it).
2. Example: height of a cylinder is 5 cm, and basis radius – 2 cm. In this case its volume will be equal: 5 * π * 2² ≈ 62.831 cm³.Число π are available on many calculators and is designated, as a rule, by the Greek letter "p" (π). On the virtual keyboard of the standard Windows calculator (in an engineering look) the number is designated as pi.
3. If instead of the radius of a cylinder its diameter is set, use the following formula: About = In * π * (D/2)² or About = ¼ * In * π * D², where D – diameter of the basis of a cylinder.
4. Example: height and diameter of the basis of a cylinder are equal to 10 cm. In this case, to learn volume, count value of the following expression: 10 * π * (10/2)² ≈ 785.398 cm³.
5. In practice, it is usually much simpler to measure perimeter (circle length) of the cylinder basis, than its diameter or radius. To count cylinder volume if the perimeter of its basis is known, use the following formula: About = ¼ * In * P²/π, where P – basis perimeter. When using this formula for calculation of capacity of a container (ware) consider that actual capacity will be a little less settlement (at a size of volume of walls of a vessel).
6. According to definition, any line on the plane can be the basis of a cylinder, and it forming it is unreliable perpendicular to the basis. Generally it is possible to recognize cylinder volume by the following rules: - the volume of a cylinder is equal to the work of length the plane forming on cylinder cross-sectional area which is perpendicular to forming; - the volume of a cylinder is equal to the work of the area of the basis on height (distance between the bases).