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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Updated on: 10-Oct-2022

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