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Cube Formula

Cube formula: Explore more about the Cube Formula with solved examples.

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.

In the above 3-D figure of the cube having side a, if one observes it from any one direction/side i.e. from top or bottom or left or right or Rear or front side we can resolutely conclude that it is a square as all sides are equal having a unit as its magnitude. And that’s how the total surface area of a cube is derived actually. In mathematical terms, the total surface area of cube is expressed as 6a²  and we know that area of a square is given as a2 , since there are 6 faces involved the total surface area comes out to be as 6a².

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

faq

Frequently Asked Questions

Get answers to the most common queries related to the Cube Formula.

How many edges are there in a regular cube?

Ans. There are 12 edges in any regular cube.

The volume of a cube is given by the formula?

Ans. The volume of a cube is expressed as side³.

Is a cube polygon?

Ans. No, the cube is not a polygon, but a polyhedron.

A cube is 2-D or 3-D?

Ans. Any cube is always a three-dimensional solid figure.