# A copper rod of diameter 2 cm and length 10 cm is drawn into a wire of uniform thickness and length 10 m.

Question:

A copper rod of diameter 2 cm and length 10 cm is drawn into a wire of uniform thickness and length 10 m. Find the thickness of the wire.

Solution:

We have,

the radius of the copper rod, $R=\frac{2}{2}=1 \mathrm{~cm}$,

the height of the copper rod, $H=10 \mathrm{~cm}$ and

the height of the wire, $h=10 \mathrm{~m}=1000 \mathrm{~cm}$

Let the radius of the wire be $r$.

As,

Volume of the wire $=$ Volume of the rod

$\Rightarrow \pi r^{2} h=\pi R^{2} H$

$\Rightarrow r^{2} h=R^{2} H$

$\Rightarrow r^{2} \times 1000=1 \times 10$

$\Rightarrow r^{2}=\frac{10}{1000}$

$\Rightarrow r^{2}=\frac{1}{100}$

$\Rightarrow r=\sqrt{\frac{1}{100}}$

$\Rightarrow r=\frac{1}{10}$

$\Rightarrow r=0.1 \mathrm{~cm}$

$\Rightarrow$ The diameter of the wire $=2 r=2 \times 0.1=0.2 \mathrm{~cm}$

$\therefore$ The thickness of the wire $=0.2 \mathrm{~cm}$

So, the thickness of the wire is 0.2 cm or 2 mm.