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.

Answer 1

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