To calculate the volume of any body, it is necessary to know its linear sizes. It concerns such figures as a prism, a pyramid, a sphere, a cylinder and a cone. For each of these figures there is the formula of scoping.
It is required to you
- - ruler;
- - knowledge of properties of volume figures;
- - formulas of the area of a polygon.
Instruction
1. For definition volumeof prisms find the area of one of its bases (they are equal) and increase by its height. As in the basis various types of polygons can lie, for them use the corresponding formula.V=SosnH.
2. For example, to find the volume of a prism which basis represents a rectangular triangle with legs of 4 and 3 cm and height of 7 cm make such calculations: • calculate the area of a rectangular triangle which is the prism basis. For this purpose multiply lengths of legs, and divide result into 2. Sosn of =3∙4/2=6 cm²; • increase the area of the basis by height, it also will be cm³ V=6∙7=42 prism volume.
3. To calculate pyramid volume, find works of the area of its basis on height, and increase result by 1/3 V=1/3SosnH. Pyramid height – the piece lowered from its top on the basis plane. Most often so-called regular pyramids which top is projected in the center of the basis which represents a regular polygon meet.
4. For example, to find the volume of a pyramid which cornerstone the correct hexagon with the party of 2 cm which height is 5 cm is do such actions: • on a formula S=(n/4) • a²\• ctg(180º/n) where n is the number of the parties of a regular polygon, and – length of one of the parties, find the area of the basis. S=(6/4)•2²\• ctg(180º/6) of ≈10.4 cm²; • calculate pyramid volume by cm³ formula V=1/3SosnH=1/310,4∙5≈17,33.
5. The volume of a cylinder find the same as prisms, through the work of the area of one of the bases on its height V=SosnH. When calculating consider that the basis of a cylinder represents a circle which area is equal to Sosn =2 ∙π ∙ to R² where π ≈ 3.14, and R is the radius of a circle which is the cylinder basis.
6. Find cone volume by analogy with a pyramid on a formula V=1/3SosnH. The basis of a cone is the circle which area find as it is described for a cylinder.
7. The volume of a sphere depends only on its radius of R and is equal V=4/3 ∙π ∙ to R³.