Find the volume of a cube whose surface area is \[150{m^2}\].

Hint:
Here, we will use the formula of surface area of a cube to find the length of the side of the cube. We will then substitute the value of length in the formula volume of a cube. We will simplify it further to find the required volume of a cube.

Formula Used:
We will use the following formulas:
1) Surface area of a cube is given by the formula \[S.A. = 6{a^2}\] where \[a\] is the side of the cube.
2) Volume of a cube is given by the formula \[V = {a^3}\]

Complete step by step solution:
We are given that the surface area of a cube is \[150{m^2}\].
\[S.A. = 150{m^2}\]
Using the formula of surface area of a cube, \[S.A. = 6{a^2}\], we get
\[ \Rightarrow 6{a^2} = 150\]
Dividing both the sides by 6, we get
\[ \Rightarrow {a^2} = \dfrac{{150}}{6}\]
\[ \Rightarrow {a^2} = 25\]
By taking square root on both the sides, we get
\[ \Rightarrow a = 5\]
Now we will find the volume of a cube.
Substituting \[a = 5\] in the formula \[V = {a^3}\], we get
\[V = {5^3}\]
Applying the exponent on the terms, we get
\[ \Rightarrow V = 125\]

Therefore, the volume of a cube is \[125{m^3}\].

Note:
We know that Volume is defined as the quantity of substance that can be contained in an enclosed curve or a container. A cube is a three dimensional figure and it is bounded by squares on all the sides. The properties of a cube include that it has all its faces in the shape of a square. All the faces or sides have equal dimensions. The difference between the square and the cube is square is a two-dimensional figure with two dimensions length and breadth whereas the cube is a three-dimensional figure with three dimensions length, breadth and height.