Question

The diameter of a copper sphere is $6cm$. It is beaten and drawn into a wire of diameter $0.2cm$. The length of wire is ........

• A. $36cm$
• B. $360cm$
• C. $3600cm$
• D. None

Answer 1

The correct option is C $3600cm$

The wire is in the shape of a cylinder.
Since the sphere is melted and a cylindrical wire is formed, their volumes are equal.
Volume of a sphere of radius 'r' $=n\frac{4}{3}\pi r^3$

As the diameter of the sphere is $6$ cm, its radius r $=3$ cm
Volume of a cylinder of radius "R" and height "h" $=\pi R^{2}h$
Radius of the wire $\frac{0.2}{2}=0.1cm$

Hence, Volume of sphere $=$ Volume of the wire
$\frac{4}{3}\pi r^3=\pi R^{2}h$

$\frac{4}{3}\pi \times 3^3=\pi \times {0.1}^2\times h$

$h=3600cm$
Hence, length of the wire $=3600cm$