The volume of a sphere is 38808 cu. cm. The curved surface area of the sphere (in cm²) is:

1. 1386

2. 4158

3. 5544

4. 8316

Given,

Volume of sphere = 38808 cm³

Let the radius of the sphere be r cm.

By formula,

Volume of sphere = $\dfrac{4}{3}$ πr³

$\Rightarrow \dfrac{4}{3} \times \dfrac{22}{7} \times \text{r}^3 = 38808 \\[1em] \Rightarrow \text{r}^3 = \dfrac{38808 \times 7 \times 3}{22 \times 4} \\[1em] \Rightarrow \text{r}^3 = \dfrac{814968}{88} \\[1em] \Rightarrow \text{r}^3 = 9261 \\[1em] \Rightarrow \text{r} = \sqrt[3]{9261} \\[1em] \Rightarrow \text{r} = 21 \text{ cm}.$

Curved surface area of sphere = 4πr²

= 4 × $\dfrac{22}{7}$ × 21 × 21

= 4 × 22 × 3 × 21

= 5544 cm².

Hence, option 3 is the correct option.