Question

In a closed wooden box, length $=20$ cm, breadth $=14$ cm, height $=10$ cm and thickness $=5$ mm. If weight of empty box is $3.462$ kg, what is the weight of $1\text{ cm^3$ of wood?}

• A. 4 grams
• B. 5 grams
• C. 6 grams
• D. 7 grams

Hint:

For hollow boxes, wood volume $=$ (outer volume) $-$ (inner volume). Convert thickness to the same unit and subtract twice the thickness from each outer dimension to get inner dimensions.

Answer 1

The Correct Option is C

Thickness $=5$ mm $=0.5$ cm.
Outer volume $=20\times 14\times 10=2800\ \text{cm}^3$.
Inner dimensions $=(20-1)\times(14-1)\times(10-1)=(19\times 13\times 9)$ (subtract thickness on both sides).
Inner volume $=19\cdot 13\cdot 9=2223\ \text{cm}^3$.
Wood volume $=2800-2223=577\ \text{cm}^3$.
Weight of box $=3.462$ kg $=3462$ g. Hence density \[ \frac{3462\ \text{g}}{577\ \text{cm}^3}=6\ \text{g/cm}^3. \] \[ \boxed{6\ \text{grams per cm}^3} \]