Cube is a special case of cuboid in which all the dimensions - length, breadth and height are equal. Since every real object occupies some space. It is usually specified by its three dimensions-length, breadth and height (depth or thickness). It may be solid or hollow object. In case of circular, cylindrical and spherical object the specifying object may change to radius, angles etc. It unit of measurement is cubic units.

## Volume of a Cube Formula

Volume enclosed by a cube is the number of cubic units that will exactly fill a cube. The amount of space occupied by the object is called volume. It unit of measurement is m3, cm3, inches3 etc. Volume of a cube is side times side times side. Since each side of a square is the same, it can simply be the length of one side cubed.

Formula:

Volume of the Cube = (Side)3

## How to Find the Volume of a Cube

A cube is a three-dimensional solid object bounded by six square faces, 12 sides, with three meeting at each vertex. To find the volume of a cube, or a rectangular shaped solid, just multiply three times the length of one side of a cube.

Steps for Finding the Volume of a Cube:

Step 1: Measure the length of any one side of the cube, because all dimensions are equal.

Step 2: Multiply the dimension 3 times. (Volume = length * breadth * height)

Step 3: Write answer in the proper cubic unit of measurement.

Example 1:
Find the volume of a cube with side 7 inches.

Solution:
Side of a cube = 7

Volume of a Cube = (Side)3

=> Volume of a Cube =(7)3

= 7 * 7 * 7

= 343

=> Volume of a cube is 343 cubic inches.

Example 2:

Find the volume of a cube whose space diagonal length is 5$\sqrt{3}$.

Solution:

Step 1:

Let each side of the cube = a
Given:
Space diagonal of cube (D) = 5$\sqrt{3}$

Diagonal of cube (d) = $\sqrt{a^2 + a^2}$

= $\sqrt{2a^2}$

= a$\sqrt{2}$

=> d = a$\sqrt{2}$ ..........................(1)

Step 2:

Now
D = $\sqrt{d^2 + a^2}$

=> D= $\sqrt{(a\sqrt{2})^2 + a^2}$

[(using (1)]

=> D= $\sqrt{2a^2 + a^2}$

=> D = $\sqrt{3a^2}$

Step 3:

=> 5$\sqrt{3}$ = $\sqrt{3a^2}$

[ Because D = 5$\sqrt{3}$ is given ]

=> 5$\sqrt{3}$ = a$\sqrt{3}$

=> 5 = a

or a = 5, side of cube

Step 4:

Volume of a cube = (Side)3

=> Volume of a cube = 53 = 125

Hence, volume of cube 125 cube unit.