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Question
The diameter of a sphere is 42 cm. It is melted and drawn into a cylindrical wire of diameter 2.8 cm. Find the length of the wire.
Solution
Radius of the sphere `=42/2 = 21 "cm"`
volume of sphere`=4/3pi"r"^3`
`=(4/3pixx21xx21xx21) "cm"^3`
Radius of the wire `=2.8/2 = 1.4 "cm" `
Let the length of the wire be h cm. then,
Volume of the wire= πr2h
`=(pixx14/10xx14/10xx"h")"cm^3"`
Therefore
`4/3 pixx21xx21xx21=pixx14/10xx14/10`
`=>12348=(49/25)xx"h"`
`=> "h" = 6300 "cm"`
`=> "h" =(6300/100) "m"`
⇒ h = 63 m
Hence, the length of the wire is 63 m.
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