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Question
A copper wire of diameter 6 mm is evenly wrapped on a cylinder of length 18 cm and diameter 49 cm to cover its whole surface. Find the length and the volume of the wire. If the density of copper be 8.8 g per cm3, then find the weight of the wire.
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Solution
We have,
Diameter of the coppe wire, d = 6 mm = 0.6 cm,
Radius of the copper wire, `r = 0.6/2 = 0.3 "cm",`
Length of the cylinder, H = 18 cm,
Radius of the cylinder, `"R" =49/2`
The Number of rotations of the wire on the cylinder`= "Length of the cylinder, H"/ "Diameter of the copper wire, d"`
`= 18/0.6`
= 30
The circumferences of the base of the cylinder `= 2piR = 2xx22/7xx49/2 = 154 "cm"`
So, the of the wire, h = 30 × 154 = 4620 cm = 46.2 m
Now, The volume of the wire = πR2
`= 22/7xx0.3xx0.3xx4620`
= 1306.8 cm3
Also, the weigt of the = Volume of the wire × Density of the wire
= 1306.8 × 8.8
= 11499.84 g
≈ 11.5 kg
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