Question

The external dimensions of a wooden box are 18 cm, 10 cm and 6 cm respectively and thickness of the wood is 5 mm. If the empty box weighs 3.15 kg, then the weight of $1c{m}^3$ of wood is ________.

• A. 7 grams
• B. 15 grams
• C. 10 grams
• D. 1 grams

Answer 1

The correct option is C

10 grams

External volume of cuboid,
$V=lbh$
$V=18\times 10\times 6c{m}^3$
$V=1080{\text{cm}}^3$

Thickness, $t=0.5\text{cm}$. Internal dimensions =

External dimensions - 2 x thickness
$⟹l^{\prime }=18–1=17\text{cm}$,
$b^{\prime }=10–1=9\text{cm}$,
$h^{\prime }=6–1=5\text{cm}$.

Internal volume,
$V^{\prime }=17\times 9\times 5c{m}^3$
$V^{\prime }=765{\text{cm}}^3$

Volume of wood = external volume – internal volume
$V_w=V-V$
$V_w=1080–765{\text{cm}}^3$
$V_w=315{\text{cm}}^3$

Mass of 1 cm${}^3$ of wood,
$m=\frac{\text{Weight of the empty box}}{\text{Volume of the wood}}$
$m=\frac{3.15}{315}\text{kg}$
$m=\frac{3150}{315}\text{grams}$
$m=10\text{grams}$