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How many silver coins, 1.75 cm in diamet...

How many silver coins, 1.75 cm in diameter and of thickness 2 mm, must be melted to form a cuboid of dimensions `5. 5 c mxx10 c mxx3. 5 c m`?

Text Solution

Verified by Experts

The correct Answer is:
`400.`
`"Radius of each coin, "r=(1.75/2)cm=(175/200)cm=7/8cm.`
`"Thickness of each coin, h = 2 mm"=(2/10)cm=1/5cm.`
`"Volume of each coin"=pir^(2)h=(22/7xx7/8xx7/8xx1/5)cm^(3)=(77/160)cm^(3)`.
`"Volume of the cuboid "= (5.5xx10xx3.5) cm^(3)`
`=192.5 cm^(3)`
`:." number of coins"=("volume of the cuboid")/("volume of each coin")`
`=192.5xx160/77=400.`
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