Question

A cube of side $5cm$ is cut into $1cm$ cubes. The percentage increase in volume after such cutting is __________.

Answer 1

Explaination for the correct answer:

We know that, when we make one shape from the other shape, then their volume is equal. then,

$\mathrm{The}\mathrm{number}\mathrm{of}\mathrm{small}\mathrm{cubes}=\frac{\mathrm{volume}\mathrm{of}\mathrm{bigger}\mathrm{cube}}{\mathrm{Volume}\mathrm{of}\mathrm{small}\mathrm{cube}}$

The number of cubes = $=\frac{5^3}{1^3}$

The number of cubes = $=125$

Now,

$Volumeofbiggercube=a^3$

Volume of cube = $=5^3\Rightarrow 125$

$Volumeofsmallercube=a^3$

Volume of smaller cube $=1^3\Rightarrow 1c{m}^3$

Now, $Volumeof125smallercubes=125\times 1=125c{m}^3$

Since, it is clearly seen that both the volumes are same.

Hence, it is clearly seen that their is no change in the volume.