Question

A copper wire of diameter $6mm$ is evenly wrapped on a cylinder of length $15cm$ and diameter $49cm$ to cover its whole surface. Find the length and volume of the wire. If the specific gravity of copper is $9$ grams per cubic cm. Find the weight of the wire

Answer 1

Diameter of copper wire $=6mm$
Therefore, its radius $=3mm$
Length of cylinder $=15cm=150mm$
Diameter of cylinder $=49cm=490mm$

Number of turns of copper wire $=\frac{150}{6}=25$

Length of wire in one turn $=2\pi r=2\pi \left(\frac{490}{2}\right)$
$=490\times \frac{22}{7}$
$=1540mm$

So, total length of copper wire $=25\times 1540mm$
$=38500mm$

Therefore, volume of copper wire $=\pi \times 3^2\times 38500$
$=1089000m{m}^3$

Volume ( in cubic centimeters ) $=1089c{m}^3$ [$\because 1m{m}^3=\frac{1}{{10}^3}c{m}^3$]

Specific gravity of wire $=9g/c{m}^3$

So, weight of wire $=$ Volume of wire $\times$ Specific Gravity of wire

$=(1089\times 9)g$
$=9801g$ or $9.801kg$