THE VOLUME OF CUBE AND CUBOID

Learn about the volume of Cube and Cuboid

Cuboid and Cube are 3-dimensional figures which have 6 faces, 8 vertices, and 12 edges. The point of difference between a cube, and a cuboid is that the former has all the sides equal whereas, the latter has different lengths, breadth, and height. The properties of both shapes are different despite looking almost the same. Formulas for the volume and the area of both cube and cuboid are different from one another.

We come across various cubical shaped objects in our everyday life, from a matchbox, chalk box to a book. If we observe them mathematically, these objects are either in the shape of a cube or a cuboid. The capacity of these shapes is the volume occupied by them.

CUBOID: MEANING AND VOLUME  

It is a polyhedron and consists of 6 faces, 8 vertices, and 12 edges. The faces in a cuboid are rectangular and opposite faces are equal in area. The vertices are at a 90 degree angle. The best example to recognize a cuboid is a book.

The volume of the cuboid is the space occupied by it. The product of its length(l), breadth(b), and height(h) gives its volume.

Volume =  l × b × h

The SI unit of the volume of a cuboid is or cubic meters.

Example: If the length, breadth, and height of a cuboid are 6 m, 8 m, and 5 m respectively. Calculate the volume of the cuboid.

Solution: Given, l = 6 m, b = 8 m, and h = 5 m.

Volume = l × b × h

              = 6 × 8 × 5

              = 240 m^3

The volume of the given cuboid is 240 m^3.

CUBE: MEANING & VOLUME

It’s a 3-dimensional shape consisting of 6 faces, 8 vertices, and 12 edges. The faces of the cube are square and have equal dimensions. A cube is a combination of 6 identical squares fused at the edges to form a 3-dimensional structure.

The volume of a cube is similar to that of a cuboid. The product of its length, breadth, and height gives the volume. As the cube has identical sides of equal magnitude, so the volume is equal to the cube of its side.

Volume = l × b × h

Since length, breadth, and height all are equal, we can write,

Length = breadth = height = a

‘a’ is the side of the cube. We can rewrite the above formula as,

Volume =a\times a\times a=a^3

One can easily calculate the volume of the cube by finding out the cube of the sides. For a cube with a side 1 m, the volume comes out to be 1m^3.

Example: Calculate the volume of the cube with side 5 m.

Solution: Given

Volume = a × a × a = 5 × 5 × 5 = 125 m^3

The volume of the given cube is 125 m^3.

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