Q. 214.5( 61 Votes )

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

Answer :

Given that,

External length = 36 cm

External width = 25 cm

External height = 16.5 cm

We know that,

Volume of cuboid = Length × Breadth × Height

Therefore,

External volume of the box = 36 × 25 × 16.5

= 14850 cm^{3}

It is also given that,

Thickness of iron = 1.5 cm

Therefore,

Internal length = 36 – (1.5 × 2) = 33 cm

Internal width = 25 – (1.5 × 2) = 22 cm

Internal height = 16.5 – 1.5 = 15 cm (As the box is open)

As we know that,

Volume of cuboid = Length × Breadth × Height

Therefore,

Internal volume of the box = 33 × 22 × 15

= 10890 cm^{3}

Hence,

Volume of iron = External volume – Internal volume

= 14850 – 10890

= 3960 cm^{3}

Also given that,

1 cm^{3} of iron = 8.5 grams

Therefore,

Total weight of the box = 3960 × 8.5

= 33660 grams

= 33.66 kilograms

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