Question

Find the volume of iron required to make an open box whose external dimensions are $36cm\times 25cm\times 16.5cm$ , the box being $1.5cm$ thick throughout. If $1c{m}^3$ of iron weighs $8.5$ grams, find the weight of the empty box in kilograms.

Answer 1

Outer length of open box $=36cm$

Outer breadth $=25cm$

Outer height $=16.5cm$

Thickness of iron $=1.5cm$

$\therefore$ Inner length $=36-(2\times 1.5)=36-3=33cm$

Inner breadth $=25-(2\times 1.5)=25-3=22cm$

Inner height $=16.5-1.5=15cm$

$\therefore$ Volume of iron used in it $=$ Outer volume $-$ Inner volume

$=36\times 25\times 16.5-33\times 22\times 15$

$=14850-10890=3960c{m}^3$

Now, weight of $1c{m}^3=8.5g$

$\therefore$ Total weight $=3960\times 8.5g$

$=33660g$

$=33.660kg$ [$1kg=1000g$]

The weight of the empty box is $33.660kg$.