Find the volume of a sphere whose surface area is 154 cm².

We know that Surface area of sphere = 4πr².

Given,
Surface area of sphere = 154 cm².

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

Volume of sphere = $\dfrac{4}{3}πr^3$

Putting values in equation we get,

Volume of sphere =

$\dfrac{4}{3} \times \dfrac{22}{7} \times (3.5)^3 \\[1em] = \dfrac{4 \times 22 \times 42.875}{21} \\[1em] = \dfrac{3773}{21} \\[1em] = \dfrac{539 \times 7}{3 \times 7} \\[1em] = \dfrac{539}{3} \\[1em] = 179\dfrac{2}{3} cm^3.$

Hence, the volume of sphere = $179\dfrac{2}{3}$ cm³.