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A closed wooden box 80 cm long, 65 cm wide and 45 cm high, is made of 2.5-cm-thick wood. Find the capacity of the box and its weight if 100 cm3 of wood weighs 8 g.

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Given that, 

External length = 80 cm 

External width = 65 cm 

External height = 45 cm 

We know that, 

Volume of cuboid = Length × Breadth × Height 

Therefore, 

External volume of the box = 80 × 65 × 45 

= 234000 cm3 

It is also given that, 

Thickness of the wood = 2.5 cm 

Therefore, 

Internal length = 80 – (2.5 × 2) = 75 cm 

Internal width = 65 – (2.5 × 2) = 60 cm 

Internal height = 45 – (2.5 × 2) = 40 cm 

As we know that, 

Volume of cuboid = Length × Breadth × Height 

Therefore, 

Capacity of box = Internal volume of the box = 75 × 60 × 40 

= 180000 cm3 

Hence, 

Volume of wood = External volume – Internal volume 

= 234000 – 180000 

= 54000 cm3 

It is also given that, 

100 cm3 of wood weighs 8 g 

Therefore, 

Weight of wood = \(\frac{54000}{100}\times8\)

= 4320 g 

= 4.32 kg

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