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Question
The diameter of a copper sphere is 18 cm. The sphere is melted and is drawn into a long wire of uniform circular cross-section. If the length of the wire is 108 m, find its diameter.
Solution
The radius of copper sphere, `R = 18/2`= 9 cm
The volume of sphere `= 4/3 pi xx (9)^3`
`= 4/3 pi xx 729`
`= 972 pi cm^2`
Since,
The sphere is melted and drawn into a long circular wire of length 108 m = 10800 cm
Let r be the radius of wire,
Clearly,
The volume of wire = volume of sphere
`pi xx r^2 xx 10800 = 972 pi`
`r^2 = (972)/(10800)`
` =9/100`
`r = 3/10`
`r = 0.3 cm`
And, d = 2r = 0.6 cm
Hence, the diameter of the wire will be equals to 0.6 cm
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