Question

How many silver coins of diameter $5cm$ and thickness $4mm$ have to be melted to prepare a cuboid of $12cm\times 11cm\times 5cm$ dimension?

Answer 1

Radius of coin $=\frac{\text{diameter}}{2}=\frac{5}{2}=2.5$

Height of coin $=4mm=0.2cm$

Therefore,

Volume of $1$ coin $=\pi r^{2}h=\frac{22}{7}\times {\left(2.5\right)}^2\times 0.2=1.25\times \frac{22}{7}$

Dimensions of cuboid $=12cm\times 11cm\times 5cm$

Therefore,

Volume of cuboid $=12cm\times 11cm\times 5cm=660{cm}^3$

Now,

Number of coins $=\frac{\text{Volume of cuboid}}{\text{Volume of 1 coin}}=\frac{660}{1.25\times \frac{22}{7}}=\frac{660\times 7}{22\times 1.25}=168$