The cube is the volume geometrical figure made of six sides ("hexahedron") of the correct form. The internal space of such polyhedron limited to sides can be calculated, having the information about some of its parameters. In simple cases there is enough knowledge of only one of them - such is feature of volume figures to sides of an identical form.
Instruction
1. If there is an opportunity to learn from statements of the problem or to measure independently length of any edge (a) of a cube, at your disposal there will be both length, and width, and polyhedron height at once. For calculation of volume (V) hexahedron multiply these three parameters, that is just cube edge length: V = a³.
2. On the area of a side (s) it is possible to calculate the volume of this figure too. As area square it is equal the second of degree of length of its party, you can express through it cube edge length: = √s. Substitute this expression in a volume formula from the previous step to receive such equality: V = (√s)³.
3. The known length of diagonal (l) of one side is the sufficient parameter for finding of volume of a cube because on Pythagorean theorem through it it is possible to express length of an edge of this volume figure: a = l/√ 2. Build this expression in the third degree to receive required size: V = (l/√ 2)³.
4. Diagonal (L) not of a separate side, but hexahedron in general is a piece which connects two tops symmetric concerning the center of a figure. Length of such piece is more than length of one edge the number of times equal to a root from the three therefore for calculation of volume of a figure divide diagonal length into a root from 3, and cube result: V = (l/√ 2)³.
5. The full surface area (S) of a hexahedron consists of six areas of sides, each of which is found by squaring of length of an edge. Use it at calculation of volume of a figure - find the edge size, having divided the total area of a surface into the six and having found a root from the received value, and then cube result: V = (√ (S/6))³.
6. If the radius (r) of the sphere entered in a cube is known to you, cube it and increase by the eight - the result will be the volume of this polyhedron: V=r³*8. Through diameter (d) of such sphere it is even simpler to express the volume as its size is equal to hexahedron edge length: V = d³.
7. The formula on the radius (R) of the sphere described about a cube is a little more difficult for calculation of volume - after its construction in the third degree and multiplication by the eight, divide the received value into a root cube from the three: V=R³*8 / (√ 3)³.