3-D Cube

3-D Cube :

In geometry, a cube is a three-dimensional solid object surrounded by six square faces or sides that all meet each vertex. The cube is also called a regular hexahedron and is one of the five platonic solids.

The cube is a special type of square prism, which is of rectangular parallel quadrilateral and trigonal trapezoidron. The cube is dual to the octahedron. It has cubical symmetry which is also known as octahedral symmetry.

A cube is a three-dimensional case of the more general concept of a hypercube. It has 11 nets. If one has to color the cube, so that none of the adjacent faces have the same color, one would need 3 colors. If the original cube has an edge length of 1, its double octahedron has an edge length √2

3-D cube geometry

In this cube – side length is a.

Total surface area = 6a2

Total Volume = a3

Face diagonal = √2a

Space diagonal = √3a

radius of circumscribed sphere = √3a /2

radius of inscribed

sphere =  a /√2

angle between faces = 90°

Since the volume of the cube is the third power of its sides a × a x a, the third powers are called cubes, by analogy with squares of second powers. A cube has the largest volume between cuboids (rectangular boxes) with a given surface area. In addition, a cube has the largest volume between cuboids with a total linear size –

length + width + height.

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