The curved surface area of a sphere is 2826 cm². Calculate its radius and hence its volume .

(Take π = 3.14)

Given, curved surface area of a sphere is 2826 cm²

Curved surface area of sphere = 4πr²

$\Rightarrow 2826 = 4 \times 3.14 \times \text{r}^2 \\[1em] \Rightarrow 2826 = 12.56 \times \text{r}^2 \\[1em] \Rightarrow \text{r}^2 = \dfrac{2826}{12.56} \\[1em] \Rightarrow \text{r}^2 = 225 \\[1em] \Rightarrow \text{r} = \sqrt{225} \\[1em] \Rightarrow \text{r} = 15 \text{ cm.}$

Volume of sphere = $\dfrac{4}{3}$ πr³

$= \dfrac{4}{3} \times 3.14 \times 15^3 \\[1em] = \dfrac{4}{3} \times 3.14 \times 3375 \\[1em] = \dfrac{42390}{3} \\[1em] = 14130 \text{ cm}^3.$

Hence, radius is 15 cm and volume of sphere is 14130 cm³.