Question

The number of coins of $1.5cm$ in diameter and $0.2cm$ thick, to be melted to form a right circular cylinder of height $10cm$ of diameter $4.5cm$ is

(a) $540$ (b) $450$ (c) $380$ (d) $472$

Answer 1

The correct option is (b): $450$

Given: Diameter of coin $=1.5cm$

Radius of coin $=\frac{1.5}{2}cm=0.75cm$

Thickness of coin $=$ height of coin $=0.2cm$

Diameter of required right circular cylinder $=4.5cm$

Radius of required right circular cylinder $=\frac{4.5}{2}cm=2.25cm$

We know that the volume of cylinder is given by $V=\pi r^{2}h$

As the coins are in the form of thin cylinder

Volume of each coin $=\pi \times (0.75{)}^2\times 0.2=0.1125\pi c{m}^3$

Volume of required right circular cylinder $=\pi \times (2.25{)}^2\times 10=50.625\pi c{m}^3$

Number of coin required $=\frac{\text{(volume of required right circular cylinder)}}{\text{(volume of each coin)}}$
$=\frac{50.625\pi }{0.1125\pi }=450$ coins