Question

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✒✒ a question⤵⤵

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✏✏ À copper wire, 3mm 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 gram per centimetre cube ( g/cm³)

Answer 1

Hey mate!!!! ❤❤❤Here's ur answer!!!!!!!!!!❤❤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.
Hope this helps you!!!!

Answer 2

the diameter of wire is 3mm

so one round covers 3mm = 0.3 cm

the length of cylinder is 12 cm

no of round to cover the cylinder = 12/0.3= 40

the length required to cover one round = circumference of cylinder

length = 2πr

r = 10/2cm

length = 2 × π × 10/2

= 10π

the length required for 40 rounds = 40 × 10π

= 400π

the volume of the copper wire = πr^2×h. (as the wire in the form of cylinder)

here h = the length of wire

volume = π × 0.3/2 × 0.3/2 × 400π

= 9 π^2

as density × volume = mass

density = 8.88

volume = 9 π^2

mass = 8.88 × 9 π^2

= 8.88 × 9 × 3.14 × 3.14

= 787.97 gram