Question

If a sphere of radius $6cm$ is melted and drawn into a wire of radius $0.02cm$ then what is the length of the wire ?

Answer 1

Given,

The radius of sphere $=6cm$

Then volume of the sphere $=\frac{4}{3}\pi r^3$

$=\frac{4}{3}\pi \times (6{)}^{3}c{m}^3$

$=\frac{4}{3}\pi \times 216c{m}^3$

$=288\pi c{m}^3$

The radius of wire $=0.02cm$

Let, the length of wire be $h$

Then volume of wire$=\pi r^{2}h$

$=\pi (0.02{)}^{2}hc{m}^3$

As per question sphere is melted into wire

So, volume of wire $=$ volume of sphere

$\therefore \pi (0.02{)}^{2}h=288\pi$

$\Rightarrow 0.0004h=288$

$\Rightarrow h=\frac{288}{0.0004}$

$\Rightarrow h=720000$

Hence, the length of the wire is $720000cm$ i.e. $7200m$