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A copper wire of 4 mm diameter is evenly wound about a cylinder whose length is 24 cm and diameter 20 cm so as to cover whole surface. Find the length and weight of the wire assuming the density to be 8.68 gm/cm3.

Asked by Topperlearning User 20th February 2014, 1:56 PM
Answered by Expert
Answer:

Length of the cylinder = 24 cm

Diameter ofcopper wire = 4 m

One round of the wire will cover the surface of cylinder by 4 mm

Therefore, the number of rounds of wire to cover the length of cylinder

Now, distance of cylinder = 20 cm

Therefore, length of wire in one round = circumference of base of the cylinder

= 2straight pir =22 over 7 cross times 20 equals 440 over 7 space c m

Length of wire for covering the whole surface of cylinder = length of wire in 60 rounds

equals 60 cross times 440 over 7 equals 3771.428 space c m

Radius of copper wire = fraction numerator 0.4 over denominator 2 end fraction= 0.2cm

Therefore, volume of wire = straight pir2h equals 22 over 7 cross times open parentheses 0.2 close parentheses squared cross times 3771.428 equals 474.122 space c u. space c m

Weight of wire = volume × density = 474.122 × 8.68 = 4115.37 gm = 4.11537 kg

Answered by Expert 20th February 2014, 3:56 PM
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