Question

The external length, breadth and height of a closed rectangular wooden box are $18cm,10cm$ and $6cm$, respectively and the thickness of wood is $\frac{1}{2}cm$. When the box is empty, it weighs $15kg$ and when filled with sand it weighs $100kg$. The weight of a cubic cm of wood and a cubic cm of sand are respectively,

• A. $\frac{1}{7}kg,\frac{1}{9}kg$
• B. $\frac{1}{21}kg,\frac{1}{9}kg$
• C. $\frac{1}{21}kg,\frac{1}{7}kg$
• D. $\frac{1}{9}kg,\frac{1}{7}kg$

Answer 1

The correct option is B $\frac{1}{21}kg,\frac{1}{9}kg$

Dimension of a closed rectangular wooden box are $18cm,10cm$ and $6cm$, respectively.
The thickness of wood is $\frac{1}{2}$cm
$\therefore$ Volume of rectangular wooden block $=18\times 10\times 6$$=1080c{m}^3$
And, volume of hollow space in rectangular wooden block $=17\times 9\times 5$$=765c{m}^3$
$\therefore$ Volume of rectangular wood $=(1080-765)c{m}^3$$=365c{m}^3$
Now, weight of empty box $=15$kg
$\therefore$ Weight of a cubic cm of wood $=\frac{15}{365}$ $=\frac{1}{21}$kg
Weight of box filled with sand $=100$kg
Weight of sand $=(100-15)$kg$=85$kg
$\therefore$ Weight of a cubic cm of sand $=\frac{85}{765}$kg$=\frac{1}{9}$kg