If the volume of a three-dimensional geometrical figure is known, in most cases it is possible to find some of its linear sizes. The main linear size of any figure are lengths of its parties, and for the sphere – radius. For various types of figures it is differently.
It is required to you
- Volumes of the measured figures, properties of polyhedrons
Instruction
1. Knowing the volume of a regular polyhedron (a convex polyhedron which parties regular polygons) it is possible to calculate its party. To find length of the party of a tetrahedron (correct tetrahedron which sides are equilateral triangles), increase its volume by 12 and divide result into root square from 2. Take a cubic root from the received number.
2. To find the party of a cube which is a hexagon which each side a square, take a cubic root from its volume. Calculate the party of an octahedron which consists of 8 triangular sides, each of which is the correct triangle, having increased its volume by 3 and having divided into a root square of 2. Take a cubic root from the received number. Find the party of the dodecahedron, polyhedron consisting of 12 correct pentagons for what divide its volume into number 7.66, and take a cubic root from result.
3. To find the radius of a sphere which volume is known increase this volume by 3 and divide consistently into numbers 4 and 3.14. Their received result take a cubic root.
4. If the figure is not a regular polyhedron, then, knowing its volume, it is possible to calculate lengths only of some of its elements. Knowing the volume and the area of the basis of a prism, it is possible to find its height. For this purpose divide value of volume into the area of the basis of h=V/S. To find other linear elements, it is necessary to know parameters of the area of the basis, for example, if it is a square, take a root from value of the area square, it also will be the party of the basis.
5. If cylinder volume is known, then it is possible to find its height, knowing radius. For this purpose consistently divide volume into number 3.14 and a square of radius of the basis. If height is known, then find basis radius, having divided volume into number 3.14 and value of height, and take a root from result square.
6. To find pyramid height through volume, divide it into the area of the basis, and increase result by number 3.