Question

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

Answer 1

We have
Diameter of the sphere $=6cm$

$\therefore$ Radius of the sphere$=\frac{6}{2}=3cm$

Volume of the sphere $=\frac{4}{3}\times \pi \times 3^3{cm}^3=36\pi {cm}^3[V=\frac{4}{3}\pi 3^3]$

Let the radius of the cross-section of wire be $r$ cm

It is given that the length of the cylindrical shaped wire is $36m$

$\therefore$ Volume of the wire $=(\pi r^2\times 3600){cm}^3[V=\pi r^{2}h]$

since metallic sphere is converted into cylindrical shaped wire. Therefore,
Volume of the wire = Volume of the sphere

$\Rightarrow r^2=\frac{36\pi }{3600\pi }=\frac{1}{100}\Rightarrow r=\frac{1}{10}cm=1mm$