Find the length of $13.2\ kg$ of copper wire of diameter $4\ mm$, when $1$ cubic cm of copper weighs $8.4\ gm$.

 Given:

A copper wire has a diameter $4\ mm$.

$1$ cubic cm of copper weighs $8.4\ gm$.

To do:

We have to find the length of $13.2\ kg$ of copper wire.

Solution:

Weight of the copper wire $= 13.2\ kg$

Diamter of the wire $= 4\ mm$

This implies,

Radius $(r)=\frac{4}{2}$

$=2 \mathrm{~mm}$

$=\frac{2}{10} \mathrm{~cm}$

Therefore,

Volume of the wire $=\frac{13.2 \times 10000}{84}$

$=\frac{132 \times 10000}{10 \times 84}$

$=\frac{11000}{7} \mathrm{~cm}^{3}$

Let $l$ be the length of the wire.

$\pi r^{2} l=\frac{11000}{7}$

$\frac{22}{7} \times \frac{2}{10} \times \frac{2}{10} \times l=\frac{11000}{7}$

$l=\frac{11000}{7} \times \frac{7}{22} \times \frac{100}{4}$

$l=12500 \mathrm{~cm}$

$l=125 \mathrm{~m}$

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Updated on: 10-Oct-2022

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