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Question
The diameter of a sphere is 6 cm. It is melted and drawn into a wire of diameter 0.2 cm. Find the length of the wire.
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Solution
Diameter of a sphere = 6 cm
Radius = 3 cm
∴ Volume = `4/3pir^3`
= `4/3 xx 22/7 xx 3 xx 3 xx 3`
= `792/7 cm^3` ...(i)
Diameter of cylindrical wire = 0.2 cm
Therefore, radius of wire =`0.2/2 = 0.1 = 1/10 cm `
Let length of wire = h
∴ Volume = πr2h
= `22/7 xx 1/10 xx 1/10 xx h cm^3`
= `(22h)/700 cm^3` ...(ii)
From (i) and (ii)
`(22h)/700 = 792/7`
`=> h = 792/7 xx 700/22`
`=>` h = 3600 cm = 36 m
Hence, length of the wire = 36 m
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