Question

How many small cubes with an edge of $20cm$ each can be just accommodated in a cubical box of $2m$ edge?

• A. $10$
• B. $100$
• C. $1000$
• D. $10000$

Answer 1

The correct option is C

$1000$

Calculate the volume of cuboid and cube

The volume of one small cube is ${\left(\mathrm{side}\right)}^3={\left(20\right)}^3=8000c{m}^3$

The volume of the cuboidal box is ${(2m)}^3=8m^3=8000000c{m}^3$

So, the total number of small cubes that can be just accommodated in the cuboidal box $=\frac{\mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{cuboidal}\mathrm{box}}{\mathrm{Volume}\mathrm{of}\mathrm{small}\mathrm{cube}}=\frac{8000000}{8000}=1000$

Hence, $1000$ small cubes can be just accommodated in a bigger cubical box, so, option (C) is the correct answer.