Question

The diameter of metallic sphere is equal to $9cm$. It is melted and drawn into a long wire of diameter $2mm$ having uniform cross-section. Find the length of the wire.

Answer 1

diameter of sphere d = 9 cm

Radius of sphere $r=d/2=4.5cm$

$\to$ diameter of wire = 2mm

Radius of wire $=\frac{d}{2}=\frac{2}{2}=1mm=R=0.1cm$

$\to$ volume of sphere = volume of wire

$\therefore \frac{4}{3}\pi \times r^3=A\times length$

$\therefore \frac{4}{3}\pi \times r^3=\pi R^2\times L$

$\therefore \frac{4}{3}\times \pi \times (4.5{)}^3=\pi \times (0.1{)}^2\times L$

$\therefore L=\frac{4\times (4.5{)}^3}{3\times (0.1{)}^2}$

$\therefore L=12,150cm$