Explanation:
In geometry, a cube is a threedimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.
The cube can also be called a regular hexahedron and is one of the five Platonic solids. It is a special kind
of square prism, of rectangular parallelepiped and of trigonal trapezohedron. The cube is dual to
the octahedron. It has cubical
symmetry (also called octahedral symmetry). It is special by being a Cuboid and a Rhombohedron.
Formulae
For a cube of edge length a,
surface area

6a^{2}

Volume

a^{3 }(Our solved example in
mathguru.com uses this concept).

face diagonal


space diagonal


radius of circumscribed sphere


radius of sphere tangent to
edges


radius of inscribed sphere


angles between faces


As the volume of a cube is the third power of its sides axaxa, third powers are called cubes, by analogy with squares and second powers.
A cube has the largest volume among cuboids (rectangular boxes) with a given surface area. Also, a cube has the
largest volume among cuboids with the same total linear size (length+width+height).
http://en.wikipedia.org/wiki/Cube
Cuboid
In geometry, a Cuboid is a solid figure bounded by six
faces, forming a convex polyhedron.
There are two competing (but incompatible) definitions of a cuboid in the
mathematical literature. In the more general definition of a cuboid, the only
additional requirement is that these six faces each be a quadrilateral, and that the undirected graph formed by the vertices and edges of
the polyhedron should be isomorphic to the graph of a cube. Alternatively, the word "cuboid"
is sometimes used to refer to a shape of this type in which each of the faces
is a rectangle (and so each pair of adjacent faces
meets in a right angle); this
more restrictive type of cuboid is also known as a right cuboid, rectangular box, rectangular hexahedron, right rectangular prism, or rectangular parallelepiped.
Rectangular
cuboid
Rectangular Cuboid


Type

Prism

Faces

6 rectangles

Edges

12

Vertices

8

Symmetry group

D_{2h} (*222)

Schlafli symbol

{}x{}x{}

CoxeterDynkin diagram


Properties

convex, zonohedron,isogonal

In a rectangular cuboid, all angles are right angles, and opposite faces of a
cuboid are equal. It is also a right rectangular prism. The term "rectangular
or oblong prism" is ambiguous. Also the term rectangular parallelepiped or orthogonal parallelepiped is used.
The square cuboid, square box, or right square prism (also ambiguously called square prism) is a special case
of the cuboid in which at least two faces are squares. The cube is
a special case of the square cuboid in which all six faces are squares.
If the dimensions of a cuboid are b and c,
then its volume is abc and its surface area is 2ab + 2bc + 2ac. (Our solved example in
mathguru.com uses this concept).
The length of the space
diagonal is
Cuboid shapes are often used for boxes, cupboards, rooms, buildings, etc. Cuboids are
among those solids that can tessellate
3dimensional space. The shape is fairly versatile in being able to contain
multiple smaller cuboids, e.g. sugar cubes in a box, small boxes in a large
box, a cupboard in a room, and rooms in a building.
http://en.wikipedia.org/wiki/Cuboid
The
above explanation is copied from Wikipedia, the free encyclopedia and is
remixed as allowed under the Creative Commons Attribution ShareAlike 3.0 Unported
License.