Question

The number of cubes of edge $4cm$ that can be cut from a cube of edge $12cm$ is

Answer 1

Let the edges of the larger and smaller cubes be $xcm$ and $ycm$ respectively.
Given, edge of the larger cube, $x=12cm$
Edge of smaller cube, $y=4cm$
$\Rightarrow$ Volume of larger cube $=(12{)}^3=12\times 12\times 12{cm}^3$
and volume of smaller cube $=(4{)}^3=4\times 4\times 4{cm}^3$
$\therefore$ Number of smaller cubes that can be cut from the bigger cube
$=\frac{\text{Volume of larger cube}}{\text{Volume of smaller cube}}$
$=\frac{12\times 12\times 12}{4\times 4\times 4}$
$=27$

Thus, the required number of cubes is $27$.