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Question

A copper rod of diameter 1 cm and length 8 cm is drawn into a wire of length 18 m of uniform thickness. Find the thickness of the wire.

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Solution

The radius of the copper rod is 0.5 cm and length is 8 cm. Therefore, the volume of the copper rod is

Let the radius of the wire is r cm. The length of the wire is 18 m=1800 cm. Therefore, the volume of the wire is

Since, the volume of the copper rod is equal to the volume of the wire; we have

V1=Vπr2×1800=π×0.52×8r2=0.25×81800=1900r=130=0.033 cm

Hence, the radius of the wire is 0.033 cm = 0.33 mm.
So, thickness = 0.33×2=0.66 mm


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