Question

How many cubic centimetres of iron are there in an open box whose external dimensions are $36cm,25cm$, and $16.5cm$, the iron being $1.5cm$ thick throughout? If $1c{m}^3$ of iron weighs $15g$. find the weight of the empty box in kilograms.

Answer 1

The external dimensions of the box are $36cm,25cm$ and $16.5cm$.
The thickness of the iron $=1.5cm$
∴ Inner length of the box $=36-1.5-1.5=33cm$
Inner breadth of the box $=25-1.5-1.5=22cm$
Inner height of the box $=16.5-1.5=15cm$
Now, the volume of iron in the open box
$=$ Volume of the outer box $-$ Volume of the inner box
$=36\times 25\times 16.5-33\times 22\times 15$ [Volume $=$ length $\times$ breadth $\times$ height]
$=14850-10890$
$=3960$ $c{m}^3$
It is given that $1c{m}^3$ of iron weighs $15g$.
∴ Weight of the empty box $=3960\times 15$
$=59400g$
$=\frac{59400}{1000}$
$=59.4kg(1kg=1000g)$

Hence, weight of the empty box is $59.4kg$.