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Question

A copper wire of diameter 6 mm is evely wrapped on a cylinder of length 18 cm and diameter 49 cm to cover its whole surface. Find the length and the volume of the wire. If the density of copper be 8.8 g per cu-cm, find the weight of the wire.

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Solution

Diameter of copper wire = 6 mm, ie its radius = 3 mm

Length of cylinder = 18 cm = 180 mm
Diameter of cylinder = 49 cm = 490 mm

Number of turns of copper wire =1806=30

length of one turn =2πr=2π(4902)=227×490=1540 mm

So total length of copper wire =30×1540=46200 mm

Therefore volume of copper wire =πr2h=π×(3)2×46200=1305612 mm3

Volume in cm3=1305.612 cm3

Specific gravity of wire =8.8 g/cm3

So weight of wire =1305.612×8.8=11489.3856=11489.38 kg


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