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Question
The radius of a sphere is 9 cm. It is melted and drawn into a wire of diameter 2 mm. Find the length of the wire in metre.
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Solution
Radius of sphere = 9 cm
Volume of sphere = `4/3pir^3`
= `4/3 xx 22/7 xx 9 xx 9 xx 9`
= `3054.857 "cm"^3 = 30.55 xx 10^-4 "m"^3` .....(i)
Diameter of cylindrical wire = 2 mm
Therefore, radius = 1 mm = 0.001 m
Let length of wire be h
∴ Volume = `pir^2h`
= `22/7 xx 0.001 xx 0.001 xx h`
= `3.142h xx 10^-6` m3 ....................(ii)
From (i) and (ii)
⇒ `3.142 xx 10^-6h = 30.55 xx 10^-4`
⇒ `h = (30.55 xx 10^-4)/(3.142 xx 10^-6)`
⇒ h = 972m
Length of the wire = 972 m
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