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

1. 380

2. 450

3. 472

4. 540

Given,

Radius of coin, r = $\dfrac{\text{diameter}}{2} = \dfrac{1.5}{2}$ = 0.75 cm

Height of coin, h = 0.2 cm

Radius of cylinder, R = $\dfrac{\text{diameter}}{2} = \dfrac{4.5}{2}$ = 2.25 cm

Height of cylinder, H = 10 cm

Let no. of coins required to be melted to form cylinder be n.

Volume of cylinder = n × Volume of each coin

∴ πR²H = n × πr²h

$\Rightarrow \text{n} = \dfrac{π\text{R}^2\text{H}}{π\text{r}^2\text{h}} \\[1em] \Rightarrow \text{n} = \dfrac{2.25^2 \times 10}{0.75^2 \times 0.2} \\[1em] \Rightarrow \text{n} = \dfrac{5.0625 \times 10}{0.5625 \times 0.2} \\[1em] \Rightarrow \text{n} = \dfrac{50.625}{0.1125} \\[1em] \Rightarrow \text{n} = 450$

Hence, option 2 is the correct option.