Question

Find the number of small cubes with an edge of 10 cm that can be accommodated in a cubical box of edge 2 m.

• A. 800
• B. 8,000
• C. 400
• D. 4,000

Answer 1

The correct option is B 8,000

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

So, Volume of the cubical box,
$V=(2\times 2\times 2)m^3$
$V=8{\text{m}}^3$

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, $n\times V=V^{\prime }$
$\Rightarrow n=\frac{V^{\prime }}{V}$
$\Rightarrow n=\frac{8}{0.001}$
$\Rightarrow n=8,000$
$\therefore$ The number of small cubes that can be accommodated in the cubical box is 8,000.