Question

The diameter of a metallic sphere is $6$ cm. The sphere is melted and drawn into a wire of uniform circular cross-section. If the length of the wire is $36$ m, find the radius of its cross-section.

• A. $0.8$ cm
• B. $0.5$ cm
• C. $0.3$ cm
• D. $0.1$ cm

Answer 1

The correct option is D $0.1$ cm

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 $=\frac{4}{3}\pi r^3$
As the diameter of the sphere is $6$ cm, its radius $r=3$ cm
Volume of a Cylinder $=\pi R^{2}h$
Length of the wire $h=36m=3600cm$
Hence, Volume of sphere $=$ Volume of the wire
$\frac{4}{3}\pi r^3=\pi R^{2}h$
$R^2=\frac{1}{100}$
$R=\frac{1}{10}=0.1cm$
Hence, radius of the cross-section of the wire $=0.1cm$