 # A closed wooden box 80 cm long, 65 cm wide and 45 cm high, is made of 2.5-cm-thick wood.

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.

Solution:

External length $=80 \mathrm{~cm}$

External width $=65 \mathrm{~cm}$

External height $=45 \mathrm{~cm}$

$\therefore$ External volume of the box $=80 \times 65 \times 45=234000 \mathrm{~cm}^{3}$

Thickness of the wood $=2.5 \mathrm{~cm}$

Then internal length $=80-(2.5 \times 2)=75 \mathrm{~cm}$

Internal width $=65-(2.5 \times 2)=60 \mathrm{~cm}$

Internal height $=45-(2.5 \times 2)=40 \mathrm{~cm}$

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

Volume of the wood $=$ external volume $-$ internal volume $=(234000-180000) \mathrm{cm}^{3}=54000 \mathrm{cr}$

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

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