**Cube Formula**

Small Description: A cube is a type of special cuboid having all three dimensions equal. Various formulas can be derived for its volume, total surface area, diagonal, etc., which we will see one by one.

As soon as the word “cube” is read, I am sure many of our reader’s minds are echoed by the famous Rubik’s cube’s image. Well, definitely, it’s not a cakewalk to solve it, but it gets significantly easier when one understands the concept behind it. Now, how can one solve the magic Cube without first knowing about the simple and conventional 3-D Cube, which is nothing but a special cuboid which has all the 3 dimensions equal, i.e., length = breadth = height.

There are several ways to define a cube and as learners of geometry we can define it as a three-dimensional solid object which is fenced in by six square faces with three meeting at each vertex.

It consists of 6 faces, 12 edges as well as 8 vertices.

**Basic Formulas**

Since a cube is a three-dimensional cuboid having all sides equal i.e., length = breadth = height = a

Volume of such a polyhedron is expressed as length×breadth×height = a×a×a= a³

Since in a cube all the 6 faces are nothing but square therefore the total surface area is given as 6×a².

Using Pythagoras theorem, the diagonal of cube having side as acomes out to be √3a

**Solved Examples**

1. The perimeter of one face of a cube is 40cm, its volume will be?

We know that, face of a cube = square only.

Perimeter = 4a = 40; a = 10

Therefore, side of cube = 10cm

And we know that, volume of cube is side³ = 10³=1000 cubic cm

2. If the side of a cube is given as 5cm then what will be its maximum surface area?

We know that surface area of cube is given as 6a²

And a = 5, therefore 6a²=6× 5²=6*25=150 sq .cm

3. What is the volume of the cube in cubic cm whose diagonal measures 83?

We know that diagonal of a cube is given by the formula 3a

Therefore √3a=8√3 , a = 8

And volume = a³= 8³=512 cubic cm