Cube call a volume geometrical figure with eight edges, twelve tops and six sides. From the parallelepiped having the same parameters it is distinguished by obligatory equality of lengths of all edges and right angles in tops of each side. Simplicity of this figure does simple calculation of total area of a surface of all its sides.
Instruction
1. If length of an edge of a cube (a) is known, then you can use the most widespread of all possible options of a formula of calculation of the area of its surface (S). By definition each side of this figure has the square form, and its area is equal to length of the side built in the second degree. As all of such sides at a cube six, this number it is necessary to increase in so many time: S = 6*a².
2. If length of an edge is unknown, but the volume (V) space limited by the parties of a cube is given, then the area (S) can be determined too. As only the size, known from conditions, for this figure is construction of length of an edge the third degree, length of the party of each side can be determined if to take a cubic root from this parameter. Substitute this expression in equality from the previous step and you receive such formula: S = 6 * ³ √ V)².
3. If length of diagonal of a cube (L) is known, then through it it is possible to express length of one side too so and to calculate hexahedron surface area. Diagonal is multiplication of length of a side by a square root from the three - express the size of one party of a square from this formula and substitute the received value in the same equality from the first step: S = 6 * (L / √ 3)² = 2*L².
4. If the radius of the sphere (R) described about a cube is known, then the formula of calculation of surface area can be removed from the expression step received on previous. As any of diagonals of a cube coincides with diameter of such sphere, and diameter is the doubled radius, you should transform a formula to such look: S = 2*(2*R)² = 8*R².
5. It is even simpler to receive a formula of calculation of surface area (S) of a hexahedron if the radius (r) of the sphere which is not described, and entered in this figure is known. Its diameter (the doubled radius) is equal to cube edge length. Substitute this value in a formula from the first step and receive such equality: S = 6 * (2*r)² = 24*r².