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Question
The diameter of a metallic sphere is equal to 9cm. it is melted and drawn into a long wire of diameter 2mm having uniform cross-section. Find the length of the wire?
Solution
Given diameter of a sphere (d) = 9cm
Radius(r) = `9/2` = 4.5cm
Volume of a sphere = `4/3pir^3`
`V_1=4/3xxpixx4.5^3=381.70cm^3` ...........(1)
Since metallic sphere is melted and made into a cylindrical wire
Volume of a cylinder = πr2h
Given radius of cylindrical wire(r) =`2mm/2`
=1mm = 0.1cm
`V_2=pi(0.1)^2h` ..........(2)
Equating (1) and (2)
V1 = V2
⇒ 381.703 = π(0.1)2h
⇒ h = 12150cm
∴ Length of wire (h) = 12150cm
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