Find 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 `5 cm` and diameter `4.5 cm.`

Explanation

Each coin is cylindrical in shape
Radius of each coin, `r = (1.5)/(2) cm = 0.75 cm`
Thickness of each coin, h = 0.2 cm
Volume of each coin `= (pi r^(2)h)` cubic units
`= (pi xx 0.75 xx 0.75 xx 0.2) cm^(3)`
Radius of the new cylinder formed, `R = (4.5)/(2) cm = 2.25 cm`
Height of the new cylinder formed, `H = 5cm`
Volume of the new cylinder formed `= pi R^(2) H`
`= (pi xx 2.25 xx 2.25 xx 5) cm^(3)`
Number of coins `= (("volume of new cylinder")/("volume of 1 coin"))`
`= ((pi xx 2.25 xx 2.25 xx 5)/(pi xx 0.75 xx 0.75 xx 0.2))`
`= ((225 xx 225 xx 5 xx 10)/(75 xx 75xx 2)) = 225`
Hence, the number of coins required `= 225.`