** **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 = 5

^{3} = 125

Hence, volume of cube 125 cube unit.