Question

A copper wire, 3 mm in diameter, is wound about a cylinder whose length is 12 cm, and diameter 10 cm, so as to cover the curved surface of the cylinder. Find the length and mass of the wire, assuming the density of copper to be 8.88 g per cm3.

Answer 1

It can be observed that 1 round of wire will cover 3 mm height of cylinder.

Length of wire required in 1 round = Circumference of base of cylinder = 2πr = 2π × 5 = 10π

Length of wire in 40 rounds = 40 × 10π

=(400 x 22)/7 =8800/7

=1257.14 cm =12.57 m

Radius of wire =0.3/2 = 0.15cm

Volume of wire = Area of cross-section of wire × Length of wire

= π(0.15)2 × 1257.14

= 88.898 cm3

Mass = Volume × Density

= 88.898 × 8.88

= 789.41 gm