How many cubic centimetres of iron are there in an open box whose external dimensions are $36\ cm, 25\ cm$ and $16.5\ cm$, the iron being $1.5\ cm$ thick throughout? If $1$ cubic cm of iron weighs $15\ g$, find the weight of the empty box in kg.
Given:
The external dimensions of an open box are $36\ cm, 25\ cm$ and $16.5\ cm$.
The thickness of the iron is $1.5\ cm$.
$1$ cubic cm of iron weighs $15\ g$.
To do:
We have to find the weight of the empty box in kg.
Solution:
External length of the open box $(L) = 36\ cm$
Breadth of the box $(B) = 25\ cm$
Height of the box $(H) = 16.5\ cm$
Width of the iron sheet used $= 1.5\ cm$
This implies,
Inner length of the box $(l) = 36 - 1.5 \times 2$
$= 36 - 3$
$= 33\ cm$
Internal breadth of the box $(b) = 25 - 2 \times 1.5$
$= 25 - 3$
$= 22\ cm$
Internal height of the box $(h) = 16.5 - 1.5$
$= 15\ cm$
Therefore,
Volume of the iron used $=$ Outer volume $-$ Inner volume
$= 36 \times 25 \times 16.5 - 33 \times 22 \times 15$
$= 14850 - 10890$
$= 3960\ cm^3$
Weight of 1 cubic cm of iron $= 15\ g$
Total weight $=\frac{3960 \times 15}{1000}$
$=\frac{59400}{1000}$
$=59.4 \mathrm{~kg}$
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