A copper wire of diameter 6 mm is evenly wrapped on a cylinder of length 15 cm and diameter 49 cm to cover its whole surface. Find the length and volume of the wire. If the specific gravity of copper is 9 gcm3, then find the weight of the wire.
Given the diameter of the copper wire is 6 mm, radius =3 mm.
Let its length be l mm.
Also given that this wire entirely wraps a cylinder of length 15 cm=150 mm and radius =492 cm=4902 mm.
Now, the curved surface of the cylinder is =2π×150×4902 mm3=231,000 mm3.
This area is entirely covered by the volume of the copper wire.
So, π×3×l=231,000 mm
or, l=24500 mm.
Now, weight of the copper wire =91000×231,000=2079 g.