Question

A solid sphere of diameter 12 cm is melted and draw into a wire of radius $\frac{1}{5}cm$ then the length of the wire is

• A. 108 m
• B. 72 m
• C. 84 m
• D. None

Answer 1

Answer: (B)

72 m

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' $=\frac{4}{3}\pi r^3$

As the diameter of the sphere is $12$ cm, its radius r $=6$ cm

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

Radius of the wire $r=\frac{1}{5}cm$

Hence, Volume of sphere $=$ Volume of the wire

$\frac{4}{3}\pi r^3=\pi R^{2}h$

$\frac{4}{3}\times 6^3={\left(\frac{1}{5}\right)}^{2}h$

$=>h=7200cm=72m$