Volume of Cube: Formula, Derivations and Solved Examples

Volume of Cube is an important and fundamental concept that is used in a variety of situations. A solid three-dimensional figure’s volume is defined as the number of cubic units it occupies. We know that all sides of a cube are equal and that the volume of a cube is equal to the product of the cube’s length, breadth, and height. The total number of cubic units occupied by a cube is defined as the volume of the cube.

A cube is a solid three-dimensional shape with six square faces. The total space occupied by an object is defined as its volume. The volume of a thing determines how much space it takes up. In this article, we have provided the definition, derivation, formula, solved examples, and other facts on the volume of cube.

What is Volume of Cube?

So, what is volume of cube? The volume of a cube is defined as the number of cubic units, occupied by the cube. The mathematical expression for the volume of the cube is given by the product of the length of the three sides of a cube.

What is Cube?

A cube is a three-dimensional solid figure with six congruent square faces. A cube has eight vertices and twelve equal length sides or edges.

What are the Dimensions of Cube?

There are three basic dimensions for a cube:

• Length (L): Generally, the length refers to the length of the front edge of the base of the cube.
• Breadth (B): Breadth is the side length perpendicular to the length and in the same plane as that of the base.
• Height (H) or Depth: Height is the side length of the cube perpendicular to the base.

Volume of Cube Formula

The volume of a cube can be determined by knowing the length of its edges. As all the edges are of equal length, the length of any one edge will be enough to calculate the volume of the cube.

Let ‘V’ be the volume of the cube and ‘a’ be the length of the edges of the cube. Then the volume will be given by:

Volume of Cube = Length × Width × Height
V = a x a x a
V = a³

Derivation For Volume of Cube

Let’s go through one of the processes through which we can derive the volume of the cube.

• Let’s start with a square surface with sides of ‘a’ units. Say it is a square sheet of paper and the first step is to find the area.
• The area of the paper is given by the product of its length and breadth. Therefore, the area of the square will be a².’
• Now a cube can be formed by stacking multiple sheets one upon the other till the height equals to ‘a’ units.
• Thus, the area of the cube can be obtained by calculating the product of the area of the square and the height.
• So, volume of cube will be given by a² x a.

Volume of Cube = a² x a = a³

Volume of Cube Using Diagonal Formula

Let’s say the length of the diagonal is given and we need to arrive at the volume of the cube. In that case, the volume of the cube can be calculated using the following formula:

Volume of Cube = √3 ×( d³/9)

Where,
d is the length of the diagonal of the cube.

Surface Area of Cube

Surface Area of Cube = 6a²

A cube has a total of 6 equal square surfaces and the sum of the area of all six faces will give us the surface area of the cube. Let ‘a’ be the side length of the cube which is also the length of each square surface. Then, the surface area of cube will be given by:

Practice Questions on Volume of Cube

Let’s go through some of the solved examples on the volume of the cube from below:

Question 01: Find the volume of the cube, having the sides of length 6 cm.
Solution: The side length of the cube is 6 cm.
We know, Volume of a cube = (length of sides of the cube)³
Thus, Volume = 6³
V = 216 cm³
The volume of the cube, having a side length of 6 cm is 216 cubic cm.

Question 02: Find the length of the edges of the cube, if its volume is equal to 343 cm³
Solution: The volume of the cube is given as 343 cm³.
Using the volume of cube formula, V = a³
Therefore, a = ³√ 343
a = 7 cm.
Therefore, the length of the cube is 7 cm.

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FAQs on Volume of Cube

Check the frequently asked questions below:

Q1. Can I calculate the volume of a cube if the diagonal length is given?
Ans. Yes, you can calculate the volume using the formula given below:
Volume of Cube = √3 ×( d³/9)

Q2. How many edges are in a cube?
Ans. There are a total of 12 edges in a cube.

Q3. What is the volume of 1 cubic unit?
Ans. The volume of a unit cube is 1 cubic unit. The cube with a length, breadth and height of 1 unit will yield into a volume of 1 cubic unit.

Q4. What is the formula of a cube?
Ans. The formula to calculate the volume of the cube is:
V = a³

Q5. What is the relationship of the volume of the cube to its edge length?
Ans. The volume of the cube and the edge length are directly related. The volume ‘V’ is directly proportional to side length ‘a’. This means that with the variation in the side length, the volume will also change.

Q6. How do you get the volume of a cube?
Ans. The volume of the cube can be calculated by finding the product of length, breadth and height of the cube.

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