Question

A copper wire 4 mm in diameter is evenly wound about a cylinder whose length is
24 cm and diameter 20 cm so as to cover the whole surface. Find the length and
weight of the wire assuming the specific density to be 8.88gm/cm3

Answer 1

Answer:

One round of wire covers 4 mm = 4/10cm in thickness of the surface of the cylinder  

Length of the cylinder = 24 cm

∴ Number of rounds to cover 24 cm = 24/4/10 = (24 × 10)/4 = 60  

Diameter of the cylinder = 20 cm  

⇒ Radius of cylinder = 10 cm  

Length of the wire in completing one round  = 2πr = 2π x 10 cm = 20 π cm.

∴ Length of the wire in covering the whole surface

= Length of the wire in completing 60 rounds  

= (20 π × 60) cm = 1200 π cm.  

Radius of copper wire = 2 mm =  2/10cm

∴ Volume of wire = ( π × 2/10 × 2/10 × 1200 π ) (π×210×210×1200π)cm3 = 48 π2 cm3

So, weight of wire = (48π2 × 8.88) gm = 426.24 π2 gm