Question

The number of small cubes with an edge of 10 cm that can be accommodated in a cubical box of edge 1 m is ___.

• A. 10
• B. 100
• C. 1000
• D. 1

Answer 1

The correct option is C 1000

We know, volume of a cube of side(edge) 'a' is $a^3$.

So, Volume of the cubical box,
$V=(1\times 1\times 1)m^3$
$V=1{\text{m}}^3$

Volume of the small cube,
$V^{\prime }=(10\times 10\times 10)c{m}^3$
$V^{\prime }=1000{\text{cm}}^3$
$V^{\prime }=0.001{\text{m}}^3$ ($\because 1{\text{m}}^3={10}^6{\text{cm}}^3$)

Let the number of small cubes be 'n'.
Then, $n\times V=V^{\prime }$
$⟹n=\frac{V^{\prime }}{V}$
$⟹n=\frac{1}{0.001}$
$⟹n=1000$
$\therefore$ Number of small cubes that can be accommodated in the cubical box is 1000.