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Question

How many silver coins(cylindrical), 1.75 cm in diameter and of thickness 2 mm, can be melted to form a cuboid of dimensions 5.5 cm × 10 cm × 3.5 cm?

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Solution

Let number of silver coins be n

Volume of cuboid = length × breadth × height = 5.5 × 10 × 3.5 = 192.5 cm3

Silver coin is a cylinder. Thickness of silver coin is height of cylinder.
Height of coin (cylinder) = h = 2 mm = 0.2 cm

Diameter of coin (cylinder) = d = 1.75 cm

Radius of silver coin (cylinder) = r=d2=1.752=0.875cm
Volume of silver coin (cylinder) = πr2h=227×0.875×0.875×0.2=0.48125cm3
According to given condition we have

n × Volume of coin = Volume of cuboid

n × 0.48125 = 192.5

192.50.48125=400


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