Question

A copper wire of diameter $6$ mm is evenly wrapped on a cylinder of length $15$ cm and diameter $49$ cm to cover its whole surface. Find the length and volume of the wire. If the specific gravity of copper is $9\frac{g}{{cm}^3}$, then find the weight of the wire.

Answer 1

Given the diameter of the copper wire is $6mm$, radius $=3mm$.

Let its length be $lmm$.

Also given that this wire entirely wraps a cylinder of length $15cm=150mm$ and radius $=\frac{49}{2}cm=\frac{490}{2}mm$.

Now, the curved surface of the cylinder is $=2\pi \times 150\times \frac{490}{2}m{m}^3=231,000m{m}^3$.

This area is entirely covered by the volume of the copper wire.

So, $\pi \times 3\times l=231,000mm$

or, $l=24500mm$.

Now, weight of the copper wire $=\frac{9}{1000}\times 231,000=2079g$.