Question

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.

Answer 1

External length = 80 cm
External width = 65 cm
External height = 45 cm

∴ External volume of the box$=80\times 65\times 45=234000c{m}^3$

Thickness of the wood = 2.5 cm

Then internal length$=80-(2.5\times 2)=75$ cm
Internal width $=65-(2.5\times 2)=60$ cm
Internal height $=45-(2.5\times 2)=40$ cm

Capacity of the box = internal volume of the box$=(75\times 60\times 40)c{m}^3=180000c{m}^3$

Volume of the wood = external volume − internal volume$=(234000-180000)c{m}^3=54000c{m}^3$

It is given that $100{\mathrm{cm}}^3\mathrm{of}\mathrm{wood}\mathrm{weighs}8\mathrm{g}.$

∴ Weight of the wood $=\frac{54000}{100}\times 8\mathrm{g}=4320\mathrm{g}=4.32\mathrm{kg}$