What do children’s blocks, an ice-cream crate, and dice have in common? Each of these objects is an example of a perfect cube. A cube is a three-dimensional shape that has squares for all six of its sides. So, how anyone finds out how big a cube is? This can be done by finding the object’s volume. Cube is a solid three-dimensional shape, which has 6 square faces or sides. We will discuss here its definition, properties and its importance in Math. Also, the student will learn the surface area and volume formula for the cube. In this topic, we will discuss the cube definition and cube formula. Let us start!

**Cube Formula**

**What is a Cube?**

We have seen 3 × 3 Rubik’s cube, which is the most common example in the real-life. In the same way, we will come across many real-life examples, such as six-sided dices, etc. Solid geometry is covering many three-dimensional shapes and figures, which have surface areas and volumes.

A cube is a 3-dimensional solid shape, which has 6 sides. Also, it has 8 vertices and 12 edges such that 3 edges meet at one vertex point. We also referred to as a square parallelepiped, an equilateral cuboid, and a right rhombohedron. So the cube is a three-dimensional structure that is formed when six identical squares bind to each other in closed form.

### Some Important Cube Formula

Some major formulas for cube which popularly used are as follows:

(1) The surface area of a cube can be computed as the amount of material required to cover the cube completely along with all six faces. We can compute the surface area of the cube is:

S = 6 × a²

Where,

S | The surface area of the cube |

A | Length of the side of a cube |

(2) The volume of any cube can be computed as the amount of space the cube takes up or as the amount of space inside of the cube. We can compute the volume of the cube is:

V = a³

Where,

V | Volume of cube |

a | Length of the side of a cube |

(3) Length of Diagonal of Face of the Cube = \( \sqrt{2} a \)

Where a is the length of the side of the cube.

(4) Length of Diagonal of Cube = \( \sqrt{3} a \)

Where a is the length of the side of a cube.

**Solved Examples**

**Q.1: **If the value of the side of the cube is 10cm, then find its surface area and volume.

**Solution:**

Given, side of a cube, a = 10cm

Therefore, by using the surface area and volume formula of the cube, we can write;

Surface Area = 6 × a²

= 6 × 10²

= 6 × 100

= 600 square cm

Also, Volume =

= a³

= 10³

= 1000 cubic cm

**Q.2:** An object of cube shape has been given. Its side length is 12 m. Find out the length of rod with a maximum length which can be kept in this object?

Solution:

Maximum Length of the rod will be the diagonal of the cube.

So,

Diagonal of cube,

= \( \sqrt{3} a \)

= \( \sqrt{3} 12 meter \)

= 12 \( \sqrt{3} meter \)

= 20.78 meter