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.

Given

Radius of copper wire (r) = 3/2 mm = 3/20 cm

Height of cylinder (H) = 12 cm

Radius of Cylinder (R) = 10/2 = 5 cm

Find out

We have to find the cost of the length and mass of the wire

Solution

The length of copper wire needed for one round will be the circumference of cylindrical circle end = 2πR =2π(5)

length of each round = 10π cm

To completely cover the cylinder with wire-no of rounds (n) of copper wire should be:

n = height of cylinder / diameter of copper wire

n = 12/3/10=120/3

number of rounds = 40

The total length of copper wire will be:

h = no. of rounds × length of each round

h = 40×10π

h = 400×3.14

h = 1256 cm

Volume of copper wire = πr2h

=π×(3/20)2×1256

= 88.82 cm3

For 1cm3 = 8.88 g of wire

so, for 88.82 cm3 = 8.88×88.82 g

Mass of copper wire = 788.7216 g

Answer

Hence,

The length of the wire is1256 cm

The mass of the wire is 788.216 grams 

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