Question

A carton holds $45$ cubical gift boxes with a side of $6$ cm each. If the length and width of the carton is $20$ cm and $15$ cm respectively, what will be its height (in cm) ?

Answer 1

The amount of material that the carton holds is the volume of the carton. In this case, it holds $45$ smaller boxes with $s=6$ cm.
Thus the volume of the carton $=$ volume of $45$ smaller boxes $=45\times$ volume of a single small box.

Volume of one small gift box $=s\times s\times s=6\times 6\times 6=216$ cm${}^3$
$\therefore$ Volume of the carton $=45\times 216=9720$cm${}^3$

Also, length of the carton $l=20$ cm and breadth of the carton $b=15$ cm
$\therefore$ Volume of the carton $=l\times b\times h=20\times 15\times h$

We previously calculated the volume to be $9720$ cm${}^3$

$⟹20\times 15\times h=9720$

$⟹h=\frac{9720}{20\times 15}$

$⟹h=\frac{9720}{300}$

$⟹h=32.4$ cm