Get dimensions of inner boxes

Question

I have a box of dimensions $L$,$W$ and $H$. Within the box, I have $Q$ number of other boxes with the same ratio of dimensions. How can I find out what the dimensions of the inner boxes are assuming the inner boxes are uniform in size and perfectly fill the box?

Answer 1

Just divide by the cube root of $Q$

E.g. if $Q=1000$, then the dimensions of the little boxes will be $\frac{1}{10}$ of the dimensions of the big box, i.e. their length is $\frac{L}{10}$, their width $\frac{W}{10}$, and their height $\frac{H}{10}$.