How many coins 1.75 cm in diameter and 2 mm thick must be melted to fo

1.	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?
Answer» 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 cm³ 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

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?

Answer»

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 cm³

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