$2.2$ cubic dm of brass is to be drawn into a cylindrical wire $0.25\ cm$ in diameter. Find the length of the wire.

Given:

$2.2$ cubic dm of brass is to be drawn into a cylindrical wire $0.25\ cm$ in diameter. 

To do:

We have to find the length of the wire.

Solution:

Let $l$ be the length of wire.

Volume of brass $=2.2$ cubic dm

Diameter of the wire $=0.25 \mathrm{~cm}$

$\Rightarrow Radius =\frac{0.25}{2}$

$=0.125 \mathrm{~cm}$

$=\frac{125}{1000}$

$=\frac{1}{8}\ cm$

Volume of the wire $=$ Volume of the brass

$=2.2 \mathrm{dm}^{3}$

$=2.2 \times 1000 \mathrm{~cm}^{3}$

$=2200 \mathrm{~cm}^{3}$

Therefore,

$\pi r^{2} \times l=2200$

$\Rightarrow \frac{22}{7} \times(\frac{1}{8})^{2} \times l=2200$

$\Rightarrow \frac{22}{7} \times \frac{1}{64} \times l=2200$

$\Rightarrow l=\frac{2200 \times 64 \times 7}{22}$

$\Rightarrow l=44800 \mathrm{~cm}$

$\Rightarrow l=\frac{44800}{100} \mathrm{~m}$

$\Rightarrow l=448 \mathrm{~m}$

The length of the wire is $448\ m$.