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A copper rod of radius 1 cm and length 2 cm, is converted into 18 meter long circular wire. Find the thickness of the wire.

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Given

Radius of copper rod (r) = 1 cm

Length of the copper rod (l) = 2 cm

∴ Volume of copper rod = πr2h = π × (1)2 × 2

= 2 π cm3

the Length of the wire (l1) = 18 meter

= 1800 cm

If the radius of transverse section of wire be R

The volume of wire = πR2h = πR2 × 1800

R = \(\frac { 1 }{ 30 }\) cm

Diameter of wire = 2R = 2 × \(\frac { 1 }{ 30 }\) = \(\frac { 1 }{ 15 }\) cm

Hence, the thickness of the wire 

= diameter = \(\frac { 1 }{ 15 }\) cm 

= 0.67 cm(approx)

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