Question

A solid sphere of radius $3cm$ is melted and then recast into small spherical balls each of diameter $0.6cm$. Find the number of balls.

Answer 1

Total volume of material would remain same.

Let radius of big sphere $=r$, small spheres $=r^{\prime }$

$\Rightarrow \frac{4}{3}\pi r^3=n\times \frac{4}{3}\pi r^{13}$

$\Rightarrow n={\left(\frac{r_3}{r_1}\right)}^3={\left(\frac{3}{\frac{0.6}{2}}\right)}^3={\left(\frac{3}{0.3}\right)}^3={10}^3$

$\Rightarrow n=1000$ [n$=$ no. of balls].