Question
How many cubic centimetres of iron is required to construct an open box whose external dimensions are 36cm, 25cm and 16.5cm provided the thickness of the iron is 1.5cm. If one cubic cm of iron weighs 7.5g, find the weight of the box.
✓
Answer
| External dimenesions | Internal dimenesions |
| $l_2 = 39cm$ | $l_1 = 36 - 1.5 - 1.5 = 36 - 3 = 33cm$ |
| $b_2 = 25cm$ | $b_1 = 25 - 3 = 22cm$ |
| $h_2 = 16.5cm$ | $h_1 = 16.5 - 15 = 15cm$ |
Volume of iron in the open box
$= l_2b_2h_2 - l_1b_1h_1$
$= (36 \times 25 \times 16.5) - (33 \times 22 \times 15)$
⇒ Volume of iron in the open box
$=9\times5\times11\Big[\frac{4\times5\times15}{10}-22\Big]$
$=45\times11[30-22]=495\times8=3960\text{cm}^3$
Volume of iron is $3960cm^3.$
So, $3960cm^3$ of iron will weigh $\frac{3960\times75}{10}=396\times75\text{gm}$
$=\frac{396\times75}{1000}\text{kg}=\frac{297}{10}\text{kg}$
Hence, the weight of the box = 29.7kg.
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