Question

A copper rod of diameter $1$ cm and length $8$ cm is drawn into a wire of length $32$ m of uniform thickness (diameter). Find the thickness of the wire.

• A. $0.05$ cm
• B. $0.01$ cm
• C. $0.10$ cm
• D. $0.03$ cm

Answer 1

The correct option is A $0.05$ cm

Both the rod and the wire are in the shape of a cylinder.

As the rod is melted and recasted in to a wire, their volumes are equal.

Volume of a Cylinder of Radius "$R$" and height "$h$" $=\pi R^{2}h$

Radius of the rod $=\frac{1}{2}$ cm

Length of the wire $=32$ m $=3200$ cm

Let $r$ be the radius of the wire formed.

$\pi \times {\left(\frac{1}{2}\right)}^2\times 8=\pi \times r^2\times 3200$
$r=\frac{1}{40}=0.025$ cm

Hence, thickness of the wire $=0.025\times 2=0.05$ cm