Question

The diameter of a sphere is $6cm$. It is melted and drawn into a wire of diameter $0.2cm$. Find the length of the wire.

Answer 1

Diameter of metallic sphere $=6cm$

$\therefore$ Radius of metallic sphere $\left(r_1\right)=3cm$

Also, diameter of cylindrical wire $=0.2cm$

$\therefore$ Radius of cylindrical wire $\left(r_2\right)=0.1cm$

Let the length of the wire be $hcm$

According to the question,

Volume of the wire $=$ Volume of the sphere

$\Rightarrow \pi \times (r_2{)}^2\times h=\frac{4}{3}\times \pi \times (r_1{)}^3$

$\Rightarrow \pi \times {\left(\frac{1}{10}\right)}^2\times h=\frac{4}{3}\times \pi \times 27$

$\Rightarrow \pi \times \frac{1}{100}\times h=36\pi$

$\therefore h=\frac{36\pi \times 100}{\pi }cm=3600cm=36m$

Hence, the length of the wire is $36m$.