How many cubic centimetres of iron are there in an open box whose external dimensions are 36 cm,

Question:

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 cm3 of iron weighs 15 g, find the weight of the empty box in kilograms.

 

Solution:

The external dimensions of the box are 36 cm, 25 cm and 16.5 cm.

Thickness of the iron = 1.5 cm

∴ Inner length of the box = 36 − 1.5 −1.5 = 33 cm

Inner breadth of the box = 25 − 1.5 −1.5 = 22 cm

Inner height of the box = 16.5 − 1.5 = 15 cm

Now,

Volume of iron in the open box

= Volume of the outer box − Volume of the inner box

= 36 × 25 × 16.5 − 33 × 22 × 15

= 14850 − 10890

= 3960 cm3

It is given that 1 cm3 of iron weighs 15 g.

$\therefore$ Weight of the empty box $=3960 \times 15=59400 \mathrm{~g}=\frac{59400}{1000}=59.4 \mathrm{~kg} \quad(1 \mathrm{~kg}=1000 \mathrm{~g})$

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