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Example:Find Volume of Cuboid from Two Cubes

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Explanation:

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

Volume

a3 (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

Rectangular cuboid

Type

Prism

Faces

6 rectangles

Edges

12

Vertices

8

Symmetry group

D2h (*222)

Schlafli symbol

{}x{}x{}

Coxeter-Dynkin 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 3-dimensional 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.