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Example: Find Volume of Cuboid

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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




6 rectangles





Symmetry group

D2h, [2,2], (*222)

Schläfli symbol


Coxeter-Dynkin diagram


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 a, b and c, then its volume is abc (Our solved example in mathguru.com uses this concept)

and its surface area is 2ab + 2bc + 2ac.

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.




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.