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Example:Finding Lateral & Total surface Area of Cube & Cuboids

 Post to:   Explanation:

Cube

In geometry, a cube is a three-dimensional 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 6a2 (Our solved example in mathguru.com uses this concept). volume a3 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

(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 = 4a2,

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