Each body has three main characteristics: weight, area and volume. If the body weight and a type of material of which it is made, a problem of calculation of volume are known it is trivial. However in a number of tasks the weight and density of a body are not given, and there are other sizes, proceeding them whom volume is required to find.
Instruction
1. Present that the body has some mass of m and density ρ. If these both parameters are known, then, applying a formula, calculate body volume as follows: V=m/ρЕсли is given density, and weight is not, find the last, knowing other parameters. For example, with the set force and the specified acceleration, use the following formula for finding of weight: m=F/asootvetstvenno, the volume of a body find on a formula: V=F/aρ where F is force of a body, an is acceleration of a body.
2. Under the terms of some tasks neither density, nor weight, nor acceleration, nor force are known, and the rectangular parallelepiped with c height, width of an and length of b is given. Height of a parallelepiped is at the same time and his edge. In such cases be guided by the fact that the volume of this figure is equal to the work of three sizes stated above: V=abc If in a task is given a cube, then as all its sides are squares, calculate volume as follows: V=a^3
3. If in a task the prism is set, then its volume is equal to the work of the area of the basis on height: V=Sosn.*NKogda in the basis of a prism is available a regular polygon, such prism is called correct. Write down a formula for the correct prism in which basis the n-square lies: V=nr^2*tgα/2*H where nr^2*tgα/2 - the area an osnovaniyaposkolka about each polygon can describe the circle having some radius, α - it is a corner between two next radiuses of a circle.
4. If in a task the pyramid with the basis and height is given, use the following ratio: Vpir.=1/3sosn. * H, where Sosn. - area of the basis. In a regular pyramid, as well as in a prism, there is a basis at which all parties are equal. Respectively, the volume of such pyramid will be: V=1/3nr^2*tgα/2*H
5. Find the volume of a sphere, proceeding from its radius or diameter: V=4/3πR^2=1/6πD^2Второе a rotation body - a cylinder - is formed at rotation of a rectangle round its pivot-center. You find its volume as follows: V=πR^2*H, where πR^2 - the area of the basis. If to rotate a rectangular triangle round its pivot-center, then the cone of the following volume will turn out: V=1/3πR^2*H