A cube is a three-dimensional shape with equal width, height, and length measurements. A cube has six square faces, and each face will have a side of equal length. Finding the volume of a cube is sometimes very much essential. Generally to find the volume of a cuboid we needed to multiply its length × width × height. In this article, we will explore the formula used to calculate the volume of a cube. The student will also gain a conceptual understanding for volume of cube formula and appropriate units to use. Let us start learning!

**Volume of a cube formula**

**What is Cube?**

What do children’s building blocks, a milk crate, and dice have all in common? Also, what is unique about the shape of their sides? All such objects are the example of a perfect cube. A cube is a unique three-dimensional shape that has squares for all six of its sides.

The volume of a cube will define the number of cubic units, that cube will occupy. A cube has a solid three-dimensional figure, which has 6 square faces or sides. Many objects like water tank, ludo dice etc are found in the shape of a cube.

**The formula for Volume of Cube:**

We can easily find the volume of the cube by knowing the length of its one edge. Suppose, the length of the edges of the cube is ‘a’. Then the V will be the product of length, height, and width. Its derivation is given below.

**Derivation for Volume of a Cube:**

The volume of an object is defined as the amount of space that a solid occupies. As we know that a cube is a 3-dimensional object with all equal sides i.e. length, breadth, and height. Cube volume formula derivation is as follows:

- Consider a square piece of paper.
- The area that square sheet will take up will be its surface area i.e. its length X breadth.
- As the square will have equal length and breadth, so the surface area will be a².
- Now, a simple cube can be made by stacking multiple square sheets on top of each other to get height as a unit.
- Hence it can be concluded that the overall area covered by the cube will be the area of the base multiplied by the height.
- So, Volume of Cube,

V = a² X a

i.e. V = a³

Where,

V | Volume of cube |

a | Length of one side |

**Solved Examples**

**Q.1:** Find the volume of a cube with sides of length 7 cm.

Solution:

Given, the length of the sides of the cube is 7cm.

We know, V = a³

Therefore, Volume, V = (7 cm)³

So, Volume V = 343 cubic cm.

**Q.2:** Find the length of the edges of the cube, if its volume is equal to 125 cubic cm.

Solution:

Given, Volume of the cube = 125 cubic cm.

Let the length of the edges is a.

We know,

The volume V = a³

Substituting the value, we get,

V = a³

Or

a = \(\sqrt[3]{V}\)

= \(\sqrt[3]{125}\)

= 5 cm

Therefore, the length of the cube is 5 cm.

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