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

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100

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1000

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Solution

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,
$V = (1 \times 1 \times 1) m^{3}$
$V = 1 m^{3}$

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

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

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