Question

If the diameter of a metallic sphere is $6$ cm, it is melted and a wire of diameter $0.2$ cm is drawn, then the length of the wire made shall be

• A. $24$ m
• B. $28$ m
• C. $32$ m
• D. $36$ m

Answer 1

The correct option is D $36$ m

Volume of a sphere of radius '$r$' $=\frac{4}{3}\pi r^3$
Radius of the sphere $=\frac{Diameter}{2}=3$ cm
The wire formed will be in shape of a cylinder.
Volume of a Cylinder of Radius "$R$" and height "$h$" $=\pi R^{2}h$
Radius of the cylinder $=\frac{Diameter}{2}=0.1$ cm
Since the sphere is melted and a cylinder is formed out of it, their volumes are equal.
$\therefore \frac{4}{3}\pi r^3=\pi R^{2}h$
$\therefore \frac{4}{3}\times 3^3={0.1}^2\times h$
$\therefore h=3600$ cm or $36$ m