Question

Find the number of coins, 1.5 cm in diameter and 2 mm thick, to be melted to form a right circular cylinder of height 10 cm and diameter 4.5 cm

Answer 1

Radius of the cylinder = `4.5/2` cm

Height of the cylinder = 10 cm

Volume of the cylinder = πr²h cu.units

= `pi xx 4.5/2 xx 4.5/2 xx 10  "cm"^3`

= `pi xx 45/20 xx 45/20 xx 10  "cm"^3`

Radius of the coin (r) = `1.5/2` cm

Thickness of the coin (h) = 2 mm = `2/10` cm

Volume of one coin = πr²h cu.units

= `pi xx 1.5/2 xx 1.5/2 xx 2/10  "cm"^3`

= `pi xx 15/20 xx 15/20 xx 2/10  "cm"^3`

Number of coins = `"Volume of the cylinder"/"Volume of one coin"`

= `(pi xx 45 xx 45 xx 10)/(20 xx 20) xx (20 xx 20 xx 10)/(pi xx 15 xx 15 xx 2)`

= `(45 xx 45 xx 10 xx 10)/(15 xx 15 xx 2)`

= `(3 xx 3 xx 10 xx 10)/2`

= 450 coins

Number of coins = 450