Question

A copper wire of diameter $6$ mm is evenly wrapped on the cylinder of length $18$ cm and diameter $49$ cm to cover the whole surface. Find the volume of the wire.

Answer 1

Diameter,$d=6mm=0.6cm$ since $1mm=0.1cm$

Radius of the wire$=\frac{0.6}{2}=0.3cm$

Length of the cylinder,$h=18cm$

Diameter of the cylinder$=49cm$

Radius of the cylinder$=\frac{49}{2}cm$

Number of rotations on the cylinder$=\frac{18}{0.6}=30$

Base circumference of the cylinder$2\pi r=2\times \frac{22}{7}\times \frac{49}{2}=154cm$

$\therefore$Length of the wire$=154\times 30=4620cm$

Volume of the wire$=\pi r^{2}h=\frac{22}{7}\times 0.3\times 0.3\times 4620=1306.8{cm}^3$