A copper wire of diameter `6mm` is evenly wrapped on a cylinder of length `15 cm` and diameter `49 cm` to cover its whole surface. Find the length and volume of the wire. If the specific gravity of copper be `9 g` per cu cm, find the weight of the wire.

Explanation

Length of the cylinder `= 15 cm` and its radius `= 24.5 cm`
Diameter of the wire `= 0.6 cm`
Number of turns `= ("length of the cylinder")/("diameter of the wire") = (15)/(0.6) = 25`
Length of wire in `1` turn = circumference of the base of cylinder
`= (2 xx (22)/(7) xx 24.5) cm = 154 cm`
Length of the wire in `25` turns = `(154 xx 25) cm = 3850 cm`
= 38.5 m
Volume of the wire `= pi r^(2)h`
`= ((22)/(7) xx 0.3 xx 0.3 xx 3850) cu cm`
`= 1089 cu cm`
Weight of the wire `= ((1089 xx 9)/(1000)) kg = 9.801 kg`