If a solid sphere of radius 10 cm is moulded into 8 spherical solid balls of equal radius, then the surface area of each ball (in cm²) is :

1. 50 π

2. 60 π

3. 75 π

4. 100 π

Let radius of small spherical balls be r cm.

Radius of sphere, R = 10 cm

Volume of solid sphere = 8 × Volume of small spherical balls

$\Rightarrow \dfrac{4}{3}π \times \text{R}^3 = 8 \times \dfrac{4}{3}π \times \text{r}^3 \\[1em] \Rightarrow 10^3 = 8 \times \text{r}^3 \\[1em] \Rightarrow 1000 = 8 \times \text{r}^3 \\[1em] \Rightarrow \text{r}^3 = \dfrac{1000}{8} \\[1em] \Rightarrow \text{r} = \sqrt[3]{\dfrac{1000}{8}} \\[1em] \Rightarrow \text{r} = \dfrac{10}{2} \\[1em] \Rightarrow \text{r} = 5 \text{ cm.}$

Surface area of small ball = 4 πr²

= 4 × π × 5 × 5

= 100 π cm².

Hence, option 4 is the correct option.