This is one of the important question as well as HOT question. Question number 33 from RS Aggarwal book page number 812, exercise 17B, chapter volume and surface area of solid.

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# 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 cm 3 , then find the weight of the wire.

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Given data,

Diameter of the copper wire, d=6 mm=0.6 cm,

Radius of the copper wire, r=0.62=0.3 cm,

Length of the cylinder, H=18 cm,

Radius of the cylinder, R=49/2 cm

The number of rotations

=180/6=30

The circumference of the base of the cylinder =2Ï€R

=2Ã— [22/7] Ã— [49/2]

=154 cm

the length of the wire, h=30Ã—154=4620 cm=46.2 m

the volume of the wire=Ï€rÂ²h

= [22/7] Ã— 0.3Â²Ã— 46.20

=1306.8 cmÂ³

the weight of the wire = Volume of the wire Ã— Density of the wire

=1306.8Ã—8.8

=11499.84 g

â‰ˆ11.5 kg