 # What will happen to the volume of a cube, if its edge is

Question:

What will happen to the volume of a cube, if its edge is

(i) halved

(ii) trebled?

Solution:

(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.