A spherical ball of lead has been melted and made into identical smaller balls with radius equal to half the radius of the original one. How many such balls can be made?

Let the radius of the spherical ball be r cm.

So, the volume = $\dfrac{4}{3} πr^3$

Radius of smaller ball = $\dfrac{r}{2}$ cm

According to question,

The volume of large spherical balls = Volume of all small balls

Let no. of small spherical balls that can be made be n.

$\therefore \dfrac{4}{3}πr^3 = n \times \dfrac{4}{3}π\Big(\dfrac{r}{2}\Big)^3 \\[1em] \Rightarrow n = \dfrac{\dfrac{4}{3}πr^3}{\dfrac{4}{3}π\Big(\dfrac{r}{2}\Big)^3} \\[1em] \Rightarrow n = \dfrac{\dfrac{4}{3}πr^3 \times 2^3}{\dfrac{4}{3}πr^3} \\[1em] \Rightarrow n = 2^3 = 8.$

Hence, 8 balls can be made.