The surface area of a sphere is 154 cm². The volume of the sphere is :

1. 359 $\dfrac{1}{3}$ cm³

2. 179 $\dfrac{2}{3}$ cm³

3. 736 $\dfrac{1}{3}$ cm³

4. 1437 $\dfrac{1}{3}$ cm³

Let radius of sphere be r cm.

Given, surface area of a sphere = 154 cm²

⇒ 4πr² = 154

$\Rightarrow 4 \times \dfrac{22}{7} \times \text{r}^2 = 154 \\[1em] \Rightarrow \text{r}^2 = \dfrac{154 \times 7}{22 \times 4} \\[1em] \Rightarrow \text{r}^2 = \dfrac{1078}{88} \\[1em] \Rightarrow \text{r}^2 = 12.25 \\[1em] \Rightarrow \text{r} = \sqrt{12.25} \\[1em] \Rightarrow \text{r} = 3.5 \text{ cm.}$

Volume of sphere = $\dfrac{4}{3}$ πr³

$= \dfrac{4}{3} \times \dfrac{22}{7} \times 3.5^3 \\[1em] = \dfrac{4}{3} \times \dfrac{22}{7} \times 42.875 \\[1em] = \dfrac{3773}{21} \\[1em] = 179\dfrac{2}{3} \text{ cm}^3.$

Hence, option 2 is the correct option.