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 10 cm and diameter 4.5 cm.

Answer

`450`

Explanation

Radius fo each cylindrical coin, `r=(1.5)/2 cm=15/20cm=3/4cm.`
thickness of each cylindrical coin, `h=2 mm = 2/10 cm = 1/5 cm.`
`"Volume of each coin ="pir^(2)h=(pixx3/4xx3/4xx1/5) cm^(3)`
`=((9pi)/80)cm^(3)`.
Radius of the required cylinder, `R, =((4.5)/2) cm = 2.25 cm`.
Height of the required cylinder, H = 10 cm.
Volume of the required cylinder
`piR^(2)H=(pixx2.25xx2.25xx10)cm^(3)`
`=(pixx(225)/(100)xx(225)/(100))cm^(3)=((405pi)/8)cm^(3)`.
`"Required number of coins "=("volume of the required cylinder")/("volume of each coin")=((405pi)/8xx80/(pi9))=450`.