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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 the copper be 8.8 g per cm3, then find the weight of the wire.
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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