The volume of a sphere is 228 π cm³. Calculate its radius and hence its surface area to nearest cm².

Given, volume of a sphere is 228 π cm³.

Let radius be r cm.

Volume of sphere = $\dfrac{4}{3}$ πr³

$\Rightarrow 228 π = \dfrac{4}{3} \times π \times \text{r}^3 \\[1em] \text{Dividing by π on both sides, we get:} \\[1em] \Rightarrow 228 = \dfrac{4}{3} \times \text{r}^3 \\[1em] \Rightarrow \text{r}^3 = \dfrac{228 \times 3}{4} \\[1em] \Rightarrow \text{r}^3 = \dfrac{684}{4} \\[1em] \Rightarrow \text{r}^3 = 171 \\[1em] \Rightarrow \text{r} = 5.55 \approx 6 \text{ cm.}$

Surface area of sphere = 4πr²

$= 4 \times \dfrac{22}{7} \times 6^2 \\[1em] = 4 \times \dfrac{22}{7} \times 36 \\[1em] = \dfrac{3168}{7} \\[1em] = 452.57 \approx 453 \text{ cm}^2.$

Hence, radius is 6 cm and its surface area is 453 cm².