Question

A spherical ball of iron has been melted and made into smaller balls. If the radius of each smaller ball is one-fourth of the radius of the original one, how many such balls can be made?

Answer 1

Let radius of big spherical ball $=r$

Then, radius of small spherical ball $=\frac{r}{4}$

Let number of small spherical balls be 'n', then

$\Rightarrow n\times$Volume of 1 small ball $=$ Volume of big ball

$\Rightarrow n\times \frac{4}{3}\pi \times {\left(\frac{r}{4}\right)}^3=\frac{4}{3}\pi r^3\Rightarrow n=\frac{r^3\times 64}{r^3}=64$