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.
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