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**Hint:**

First we draw a diagram of a cube as drawn above now we know that the volume of the cube is given as \[1{{m}^{3}}\] and the formula for the volume of the cube is:

Volume of the cube is \[L\times B\times H\]

We will take the dimension measurements as \[x\] and its cube will be equal to \[1{{m}^{3}}\].

**Complete step by step solution:**

Now as given in the question, the volume of the cube is given as \[1{{m}^{3}}\], the volume of the cube has all its height, length, width of equal length as the cube is made up of 6 square pieces with each of them having the same dimensions.

Hence, the volume of the cube is given to us as \[L\times B\times H\].

The dimension length of the length, width and height is taken as \[x\].

Hence, using the volume of cube formula and equating it with the value of \[x\], we get the value of \[x\] as:

Volume of the cube is \[L\times B\times H\] and placing the value of length, width and height is taken as \[x\], we get the value of the \[x\] as:

Volume of the cube is \[x\times x\times x\]

\[\Rightarrow 1={{x}^{3}}\]

\[\Rightarrow x=1\]m

**Therefore, the value of the sides of the cube is given as \[1\] m.**

**Note:**The volume of the cube is \[L\times B\times H\] as well as cuboid and the surface area of cube is \[6{{L}^{2}}\] with \[L=H=B\] whereas the surface area of cuboid is \[2\left( LB+BH+HL \right)\].

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