Question

$\text{How many cubic centimetres of iron are there in an open box whose external dimensions are 36 cm,25,cm and 16.5 cm,the iron being 1.5 cm thick throughout? If}1c{m}^3\text{of iron weighs 15 g, find the weight of the empty box in kilograms}.$

Answer 1

External volume (without counting hollow part) = 36* 25*16.5 = 14850 $c{m}^3$

Internal dimensions of box:

36-2(1.5) = 33cm
25-2(1.5) = 22cm
16.5-2(1.5) = 13.5cm
Volume of hollow part in box = 33 *22 *13.5 = 9801 $c{m}^3$

Box is open, therefore top part must be removed.
Volume of top part = 36*25​​​​​​​*1.5 = 1350 $c{m}^3$

Therefore, volume of box = 14850-9801-1350 = 3699 $c{m}^3$

Weight of box = 3699 *15 = 55485g = 55.485 kg