Three solid spherical beads of radii 3 cm, 4 cm and 5 cm are melted and recast into a single spherical bead. Its radius is :

1. 6 cm

2. 7 cm

3. 8 cm

4. 9 cm

Given, three spherical beads of radii 3 cm, 4 cm and 5 cm.

Volume of sphere = $\dfrac{4}{3}$ πr³

Volume of single spherical bead = Volume of bead of radius 3 cm + Volume of bead of radius 4 cm + Volume of bead of radius 5 cm

$\Rightarrow \dfrac{4}{3}π \times \text{r}^3 = \dfrac{4}{3}π \times 3^3 + \dfrac{4}{3}π \times 4^3 + \dfrac{4}{3}π \times 5^3 \\[1em] \Rightarrow \text{r}^3 = (3^3 + 4^3 + 5^3) \\[1em] \Rightarrow \text{r}^3 = 27 + 64 + 125 \\[1em] \Rightarrow \text{r}^3 = 216 \\[1em] \Rightarrow \text{r} = \sqrt[3]{216} \\[1em] \Rightarrow \text{r} = 6 \text{ cm.}$

Hence, option 1 is the correct option.