If a cylindrical rod of iron whose length is 12 times its radius is melted and cast into spherical balls of the same radius, then the number of balls will be :

1. 3

2. 6

3. 9

4. 27

Let radius of the cylinder be r cm.

Length of cylindrical rod, h = 12r

Radius of spherical balls be r cm

Number of spherical balls required be n.

Since, a cylindrical rod of iron is melted and cast into spherical balls of the same radius.

∴ Volume of cylindrical rod = n × Volume of spherical ball

$\Rightarrow π\text{r}^2\text{h} = \text{n} \times \dfrac{4}{3} π\text{r}^3 \\[1em] \Rightarrow \text{r}^2 \times \text{12r} = \text{n} \times \dfrac{4}{3} \text{r}^3 \\[1em] \Rightarrow 12\text{r}^3 = \text{n} \times \dfrac{4}{3} \text{r}^3 \\[1em] \Rightarrow 12 = \text{n} \times \dfrac{4}{3} \\[1em] \Rightarrow \text{n} = \dfrac{12 \times 3}{4} \\[1em] \Rightarrow \text{n} = \dfrac{36}{4} \\[1em] \Rightarrow \text{n} = 9.$

Hence, option 3 is the correct option.