Question

What will happen to the volume of a cube if the length of its edge is reduced to half? Is
te volume get reduced? If yes, how much?
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Answer 1

Solution:-

Let the edge of the cube be l.

∴ volume, V = $l^3$

Now, new edge, L = $\frac{1}{2} l$

∴ new volume, v = $(\frac{l}{2} )^3$ = $\frac{l^3}{8}$ = $\frac{V}{8}$                   (∵ $l^3$ can be written as V)

Now, we can see that, v = V/8

It means that the new volume is $8^{th}$ part of the original volume.

Yes, the volume is reduced by 8 times or the original volume is 8 times the new volume.