 # A copper wire of diameter 6 mm is evenly wrapped on a cylinder of length 18 cm `
Question:

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 cm3, then find the weight of the wire.

Solution:

We have,

Diameter of the coppe wire, $d=6 \mathrm{~mm}=0.6 \mathrm{~cm}$,

Radius of the copper wire, $r=\frac{0.6}{2}=0.3 \mathrm{~cm}$,

Length of the cylinder, $H=18 \mathrm{~cm}$,

Radius of the cylinder, $R=\frac{49}{2} \mathrm{~cm}$

The number of rotations of the wire on the cylinder $=\frac{\text { Length of the cylinder, } H}{\text { Diameter of the copper wire, } d}$

$=\frac{18}{0.6}$

$=30$

The circumference of the base of the cylinder $=2 \pi R=2 \times \frac{22}{7} \times \frac{49}{2}=154 \mathrm{~cm}$

So, the length of the wire, $h=30 \times 154=4620 \mathrm{~cm}=46.2 \mathrm{~m}$

Now, the volume of the wire $=\pi r^{2} h$

$=\frac{22}{7} \times 0.3 \times 0.3 \times 4620$

$=1306.8 \mathrm{~cm}^{3}$

Also, the weight of the wire $=$ Volume of the wire $\times$ Density of the wire

$=1306.8 \times 8.8$

$=11499.84 \mathrm{~g}$

$\approx 11.5 \mathrm{~kg}$