Find the number of coins, 5 cm in diameter and 0.14 cm in thickness, that are needed to be melted to form a solid cylinder of height 315 cm and radius 5 cm
Answers
Given :-
- Diameter of coins = 5 cm
- Thickness of coins = 0.14 cm
- Height of cylinder formed = 315 cm
- Radius of cylinder formed = 5 cm
To find :-
- Number of coins required
Solution :-
As the coins will be melted to form cylinder, so they will also shape as cylinder.
Now we know,
→ Volume of cylinder = πr²h
Now, we will find volume of one coin.
→ Volume of 1 coin = 22/7 × (5/2)² × 0.14
→ Volume of 1 coin = 22/7 × (2.5)² × 0.14
→ Volume of 1 coin = 22/7 × 6.25 × 0.14
→ Volume of 1 coin = 2.75 cm³
Now we will find volume of cylinder formed:-
→ Volume of cylinder = πr²h
→ Volume of cylinder = 22/7 × (5)² × 315
→ Volume of cylinder = 22/7 × 25 × 315
→ Volume of cylinder formed = 24750 cm³
Now here,
→ Number of coins = (Volume of cylinder)/(Volume of 1 coin)
→ Number of coins = 24,750/2.75
→ Number of coins = 9,000
Therefore,
Number of coins required = 9000
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Given-
Diameter of coins= 5 cm
Thickness of coins = 0.14 cm
Height of cylinder = 315 cm
Radis of cylinder = 5 cm
_________________________
To Find-
The numbers of coins
_________________________
Solution-
we know,
Volume of cylinder =πr²h
_________________________
volume of one coin
=> volume of one coin = 22/7 × (5/2)² × 0.14
=> volume of one coin = 2.75 cm³
_________________________
volume of cylinder
=> volume of cylinder = 22/7×5² × 315
=>volume of cylinder = 24750cm³
_________________________
In this case,
=> Number of coins = volume of cylinder ÷ volume of one coin
=>Number of coins = 24750/2.75