A closed box measures 66 cm, 36 cm and 21 cm from outside. If its walls are made of metal-sheet, 0.5 cm thick; find :

(i) the capacity of the box ;

(ii) the volume of metal-sheet and

(iii) weight of the box, if 1 cm^{3} of metal weighs 3.6 gm.

#### Solution

External length of the closed box = 66cm.

External breadth of the closed box = 36 cm

External height of the closed box =21 cm

External volume of the closed box= 66 x 36 x 21 = 49896 cm^{3}

Internal length of the box =(66 – 2 x 0.5) = 66 – 1 = 65 cm

Internal breadth of the box =(36 – 2 x 0.5) = 36 – 1 = 35 cm

Internal height of the box = (21 – 2 x 0.5) = 21 – 1 = 20 cm

Internal Volume of the box = 65 x 35 x 20 = 45500 cm^{3}

(i) Capacity of the box = 45500 cm^{3}

(ii) Volume of metal sheet of the box = External volume – Internal volume

= 49896 – 45500 = 4396 cm^{3}

(iii) 1 cm3 of metal weigh 3.6 grams.

Weight of the box = 4396 x 3.6 gm = 15825.6 gm