What will happen to the volume of a cube, if its edge is
(i) halved
(ii) trebled?
(i) Suppose that the length of the edge of the cube is $x$.
Then, volume of the cube $=(\text { side })^{3}=x^{3}$
When the length of the side is halved, the length of the new edge becomes $\frac{x}{2}$.
Now, volume of the new cube $=(\text { side })^{3}=\left(\frac{x}{2}\right)^{3}=\frac{x^{3}}{2^{3}}=\frac{x^{3}}{8}=\frac{1}{8} \times x^{3}$
It means that if the edge of a cube is halved, its new volume will be $\frac{1}{8}$ times the initial volume.
(ii) Suppose that the length of the edge of the cube is $x$.
Then, volume of the cube $=(\text { side })^{3}=x^{3}$
When the length of the side is trebled, the length of the new edge becomes $3 \times x$.
Now, volume of the new cube $=(\text { side })^{3}=(3 \times x)^{3}=3^{3} \times x^{3}=27 \times x^{3}$
Thus, if the edge of a cube is trebled, its new volume will be 27 times the initial volume.
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