Question

A copper wire,3mm in diameter is wound about a cylinder whose length is 12cm and diameter 10cm 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 per cm cube.

Answer 1

Solution:-

It is assumed that one round of copper wire will cover 3 mm or 0.3 cm height of cylinder.

Number of rounds = Height of the cylinder/diameter of the wire

= 12/0.3

= 40 rounds

Now,

The length of the wire required in one round = Circumference of the base of the cylinder

Diameter of the cylinder = 10 cm, so the radius = 5 cm.

circumference = 2πr

= 2*π*5

Length of wire required in one round = 10π

 Length of wire required in 40 rounds = 10π*40

= 400*22/7

= 8800/7

Length of the wire = 1257.14 cm

Radius of the wire = 0.3/2 = 0.15 cm

Volume of wire = Area of cross section of wire × length of the wire

= π*r² × 12.57

22/7 × (0.15)² × 1257.14

Volume of the wire = 88.898 cm³

Mass = Density × Volume 

= 8.88 × 88.898

Mass = 789.41 gm

Answer.

Answer 2

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