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

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

It is given in the question that,

$2.2d{{m}^{3}}$ of brass is to be drawn into a cylindrical wire of Diameter $=0.25cm$

So, radius of the wire $(r)=d/2$

$=0.25/2=0.125*{{10}^{-2}}cm$

Then, $1cm=0.01m$

Therefore, $0.1cm=0.001m$

Assume the length of the wire be (h)

As we know that,

Volume of the cylinder $=\pi {{r}^{2}}h$

Volume of cylindrical wire $=$ Volume of brass of $2.2d{{m}^{3}}$

$\frac{22}{7}{{\left( 0.125\times {{10}^{-2}} \right)}^{2}}\times h=2.2\times {{10}^{-3}}$

$h=448m$

Therefore, the length of the cylindrical wire drawn is $448m$

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