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 cm3 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 cm3


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 cm3


Hence,


Volume of iron = External volume – Internal volume


= 14850 – 10890


= 3960 cm3


Also given that,


1 cm3 of iron = 8.5 grams


Therefore,


Total weight of the box = 3960 × 8.5


= 33660 grams


= 33.66 kilograms


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