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Question 1
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.


Solution


For copper wire: Diameter = 3 mm = 0.3 cm (10mm= 1cm)
For cylinder; length h = 12 cm, d = 10 cm
Density of copper = 8.88 gm per cm3
Curved surface area of cylinder can be calculated as follows:
=2πrh
=π×10×12
=120 π cm2
Length of wire can be calculated as follows:
Length (h)=AreaWidth
=120π0.3=400π
=1256 cm
Now, volume of wire can be calculated as follows:
V=πr2h
=3.14×0.152×1256
=88.7364 cm3
Mass can be calculated as follows:
Mass=Density×Volume
=8.88×88.7364
=788g (approx)

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