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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
Solution
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
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