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 }(Our solved example in mathguru.com uses
this concept).

volume

a^{3}

face diagonal


space diagonal


radius of circumscribed sphere


radius of sphere tangent to
edges


radius of inscribed sphere


angles between faces


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.
^{ }
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 a, 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).
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.
(Our solved example in mathguru.com uses the below concept. This
is our own explanation, it is not taken from Wikipedia.)
Lateral Surface area of the cube = 4a^{2},
For a cube of edge length a
If the dimensions of a cuboid are a, b and c,
then its lateral surface area is
2 (a + b) c