Find the number of coins 1.5 cm in diameter and 0.2 cm thick to be melted to form a right circular cylinder whose height is 8 cm and diameter 6 cm.

Solution

Since shape of the coin having thickness will be like a cylinder. So, we consider coin as a cylinder.
Let r cm be the radius and h cm be the height (thickness) of a coin, then
$straight r space equals space fraction numerator 1.5 over denominator 2 end fraction cm comma space space space and space straight h space equals space 0.2 space cm$
Now, Volume of each coin
$equals space πr squared straight h equals space open parentheses straight pi space straight x space fraction numerator 1.5 over denominator 2 end fraction space straight x space fraction numerator 1.5 over denominator 2 end fraction straight x space 0.2 close parentheses space cm cubed equals space 0.225 space straight pi space space space cm cubed.$
Let R cm be the radius and H cm be the height of a cylinder, then
$straight R space equals space 6 over 2 equals 3 space cm space and space straight H space equals space 8 space cm$
Now, Volume of cylinder
$equals space πR squared straight H equals space left parenthesis straight pi space straight x space 3 space straight x space 3 space straight x space 8 right parenthesis space cm cubed equals space 72 space straight pi space space cm cubed$
Therefore,
Total number of coins = $fraction numerator Volume space of space cylinder over denominator Volume space of space one space coin end fraction$

= $fraction numerator 72 straight pi over denominator 0.225 straight pi end fraction equals 320$