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in Surface Areas And Volumes by (30.2k points)
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How many coins 1.75 cm in diameter and 2 mm thick must be melted to form a cuboid 11 cm × 10 cm × 7 cm?

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Volume of cuboid = l × b × h = 11 × 10 × 7 

Diameter of coin = 1.75 cm 

Radius = \(\frac{1.75}2\) cm = 0.875 cm 

Thickness of coin = 2 mm = 0.2 cm 

Volume of coin (cylinder) = πr2h

= (\(\frac{22}7\)) × 0.875 × 0.875 × 0.2 cm

Let number of coins be n 

⇒ n × volume of coins = volume of cuboid 

⇒ n × (22/7) × 0.875 × 0.875 × 0.2 = 11 × 10 × 7

⇒ n = \(\frac{{11} \times{10} \times{7} \times{7}}{{22} \times{0.875} \times{0.875} \times{0.2}}\)

⇒ n = 1600

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