Question

How many cubes of 10 cm edge can be put in a cubical box of 1 m edge?

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ \mathrm{Edge}\mathrm{of}\mathrm{the}\mathrm{cube},a=10\mathrm{cm}\mathrm{and} \\ \mathrm{Edge}\mathrm{of}\mathrm{the}\mathrm{cubical}\mathrm{box},l=1\mathrm{m}=100\mathrm{cm} \\ \mathrm{Now}, \\ \mathrm{The}\mathrm{number}\mathrm{of}\mathrm{cubes}\mathrm{that}\mathrm{can}\mathrm{be}\mathrm{put}\mathrm{in}\mathrm{the}\mathrm{box}=\frac{\mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{cubical}\mathrm{box}}{\mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{cube}} \\ =\frac{l^3}{a^3} \\ =\frac{{100}^3}{{10}^3} \\ ={10}^3 \\ =1000 \end{gathered}$$

So, the number of cubes that can be put in the cubical box is 1000.