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:
1) its length
2) the volume of wire

Answer 1

Diameter of copper wire = 6mm
As it covers the whole length of cylinder
The number of times it wraps around $=\frac{18cm}{6mm}=\frac{18cm}{6mm}=30$
For each turn, The length of copper wire
= Circummference of cylinder $=2\pi r=49\pi cm$
$\therefore$ For 30 turns. The total length of copper wire
$=30\times 49\times \pi$
$=30\times \text{/}{49}^7\times \frac{22}{\text{/}7}$
$=4620cm$
Volume of copper wire
= Area of cross section $\times$ length
$=\pi {\left(\frac{0.6}{2}\right)}^2\times 4620cm$
$=\frac{\text{/}{22}^{11}}{\text{/}7}\times \frac{\text{/}{0.6}^{0.3}}{\text{/}2}\times \frac{0.6}{\text{/}2}\times \text{/}{4620}^{660}c{m}^3$
$=11\times 0.3\times 0.6\times 660$
$=1306.8c{m}^3$