How many lead balls, each of radius 1.5 cm can be made by melting a bigger ball of radius 9 cm?

Given,

Radius of bigger ball, R = 9 cm

Radius of smaller ball, r = 1.5 cm

Let the number of smaller lead balls formed be n.

∴ Volume of big ball = n × Volume of each small ball

$\Rightarrow \dfrac{4}{3}π\text{R}^3 = \text{n} \times \dfrac{4}{3}π\text{r}^3 \\[1em] \text{Dividing both sides by 4π and multiplying by 3, we get :} \\[1em] \Rightarrow \text{R}^3 = \text{n} \times \text{r}^3 \\[1em] \Rightarrow 9^3 = \text{n} \times 1.5^3 \\[1em] \Rightarrow 729 = \text{n} \times 3.375 \\[1em] \Rightarrow \text{n} = \dfrac{729}{3.375} \\[1em] \Rightarrow \text{n} = 216.$

Hence, 216 lead balls can be made.