Mathematics
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) volume of metal sheet used and
(iii) weight of the box, if 1 cm3 of metal weighs 3.6 g.
Surface Area, Volume, Capacity
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Answer
(i) Given:
Outer length of the box = 66 cm
Outer width of the box = 36 cm
Outer height of the box = 21 cm
Volume of box = l x b x h
= 66 x 36 x 21 cm3
= 49,896 cm3
Thickness of metal sheet = 0.5 cm
Internal length = 66 - 0.5 - 0.5 cm = 66 - 1 cm = 65 cm
Internal width = 36 - 0.5 - 0.5 cm = 36 - 1 cm = 35 cm
Internal height = 21 - 0.5 - 0.5 cm = 21 - 1 cm = 20 cm
Volume of internal box = l x b x h
= 65 x 35 x 20 cm3
= 45,500 cm3
Hence, the capacity of the box is 45,500 cm3.
(ii) Volume of metal sheet required = 49,896 - 45,500 cm3
= 4,396 cm3
Hence, the volume of metal sheet used is 4,396 cm3.
(iii) Weight of 1 cm3 box = 3.6 g
Weight of 4,396 cm3 box = 3.6 x 4,396 g
= 15,825.6 g
Hence, the weight of the box is 15,825.6 g.
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