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Question

A copper wire of diameter 6 mm is evenly 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 the copper be 8.8 g per cm3, then find the weight of the wire.

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Solution

We have,Diameter of the coppe wire, d=6 mm=0.6 cm,Radius of the copper wire, r=0.62=0.3 cm,Length of the cylinder, H=18 cm,Radius of the cylinder, R=492 cmThe number of rotations of the wire on the cylinder=Length of the cylinder, HDiameter of the copper wire, d=180.6=30The circumference of the base of the cylinder=2πR=2×227×492=154 cmSo, the length of the wire, h=30×154=4620 cm=46.2 mNow, the volume of the wire=πr2h=227×0.3×0.3×4620=1306.8 cm3Also, the weight of the wire=Volume of the wire×Density of the wire=1306.8×8.8=11499.84 g≈11.5 kg

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