Question

How many silver coins with diameter 1.75 cm and thickness 2 mm will have to melted to recast a cuboid with dimensions 5.5 cm × 10 cm × 3.5 cm.

Answer 1

Let the number of silver coins to melt be n

The diameter of each coin = 7.5 cm

∴ Radius (r) = \(\frac { 1.75 }{ 2 }\) cm

= \(\frac { 175 }{ 200 }\) cm = \(\frac { 7 }{ 8 }\) cm

The thickness of each coin (h) = 2 mm

= \(\frac { 2 }{ 10 }\) cm = \(\frac { 1 }{ 5 }\) cm

∴ Volume of each coin = πr²h

∴ Volume of n coins = \(\frac { 77 }{ 160 }\)n cm³

Volume of cuboid = 5.5 × 10 × 3.5 = 192.5 cm³

Since the cuboid is recasted by melting the n silver coins.

⇒ Volume of n coins = Volume of Cuboid

⇒ \(\frac { 77 }{ 160 }\)n = 192.5

⇒ n = \(\frac { 192.5\times 160 }{ 77 } \) = 400

Hence, 400 silver coins will be melted.