The cylinder belongs to volume geometrical figures, to so-called bodies of rotation. Its bases are equal circles. The cylinder can be to straight lines and inclined planes.
It is required to you
- — ruler;
- — calculator.
Instruction
1. In case the area at least of one of the cylinder bases (they are equal among themselves) is known, measure its height. For this purpose lower a perpendicular from one basis of a cylinder on another and measure its length. Height of a direct cylinder is equal to any of it forming. After that find the volume as work areas of one of S cylinder bases on its height of h (V=S∙h). For example, if it is known that the area of the circle lying is equal in the basis of a cylinder to 8 cm², and its height is equal to 5 cm, then its volume will be equal to cm³ V=8∙5=40.
2. In case the area of the basis of a cylinder is unknown, its volume can be found by means of other formula. Measure cylinder height in any convenient way. Then, find diameter of the basis of a cylinder, having measured it in the convenient way, for example, by means of a ruler or a caliper. Calculate cylinder radius, having divided diameter into 2. Find the volume of this solid, having increased number π ≈ 3.14 by a square of radius of R and height of a cylinder of h (V = π ∙ R² ∙ h).
3. Example. Find the volume of a cylinder which basis has diameter of 6 cm, and height is equal to 5 cm. Determine the radius of the basis of a cylinder of R=6/2=3 cm. Calculate the volume of V = 3.14∙3² ∙ 5=141.3 cm³.
4. If a cylinder inclined, then the above formulas remain fair, but height in this case is not equal to forming. Therefore to find its volume, measure length of the forming l, and increase it by the area of the basis of S which can be found in the above way and on a sine of the angle α between forming and the plane of the basis V=S∙l∙sin(α).
5. Example. Forming a circular cylinder has length of 16 cm and is at an angle 45º to the basis. Find cylinder volume if the radius of the basis is equal to 8 cm. At first find the area of the basis of a cylinder. It is equal to S=π ∙ to R². Substitute value of this formula in expression for volume and receive V = π ∙ R² ∙ l∙sin(α) =3.14∙8² ∙ 16∙sin(45º) ≈ 2273.6 cm³.