Question

How many coins 1.75 cm in diameter and 2 mm thick must be melted to form a cuboid $11cm\times 10cm\times 7cm$ ?

Answer 1

A coin is a cylinder of diameter 1.75 cm and thickness (height of cylindrical shaped coin) is

2 mm.

$radiusofcoin=\frac{1.75}{2}cm$

$andheightofcoin=\frac{2}{10}=0.2cm$

∴ Volume of 1 coin = Volume of cylinder $=\pi r^{2}h=\pi \times (\frac{1.75}{2}{)}^2\times 0.2c{m}^3$

Dimension of cuboid are 11 cm, 10 cm and 7 cm

∴ Volume of cuboid $=l\times b\times h=10\times 11\times 7=770c{m}^3$

According to question given,

Volume of cuboid = Number of coins $\times$ Volume of each coin

$=>770=Noofcoins\times \pi \times (\frac{1.75}{2}{)}^2\times 0.2c{m}^3$

$=>Noofcoins=\frac{770}{\frac{22}{7}\times (\frac{1.75}{2}{)}^2\times 0.2}$

$=\frac{770\times 7\times 4}{22\times (1.75{)}^2\times 0.2}=\frac{980}{0.2\times 3.0625}=1600$

Hence, 1600 coins are required to form a cuboid of given dimensions.