Question

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

Answer 1

We know, $1$ m $=1000$ mm and $1$ cm $=10$ cm
Diameter of the copper Rod $=2$ cm
Radius of the copper rod $=r=1$ cm

Length of the Rod $=h=10$ cm
Length of the wire $=h=10$ m $=1000$ cm

Let suppose the radius of the wire $=R$
From the statement:

Volume of the rod = volume of the wire
$\pi r^{2}h=\pi R^{2}H$
$1\times 1\times 10=1000\times R^2$
or $R=\frac{1}{10}$ cm or $0.1$ cm

Diameter of the wire $=2r=2\times 0.1=0.2$ cm
Therefore,the thickness of the wire is $0.2$ cm or $2$ mm.