If the volume of a sphere is $179\dfrac{2}{3}$ cm³, find its radius and the surface area.

Volume of sphere = $\dfrac{4}{3}πr^3$.

Given,
Volume of sphere = $179\dfrac{2}{3}$

$\therefore \dfrac{4}{3}πr^3 = 179\dfrac{2}{3} \\[1em] \Rightarrow \dfrac{4}{3} \times \dfrac{22}{7} \times r^3 = \dfrac{539}{3} \\[1em] \Rightarrow \dfrac{88}{21} \times r^3 = \dfrac{539}{3} \\[1em] \Rightarrow r^3 = \dfrac{539 \times 21}{3 \times 88} \\[1em] \Rightarrow r^3 = \dfrac{539 \times 7}{88} \\[1em] \Rightarrow r^3 = \dfrac{3773}{88} \\[1em] \Rightarrow r^3 = 42.875 \\[1em] \Rightarrow r = (42.875)^{\dfrac{1}{3}} \\[1em] \Rightarrow r = 3.5 \text{ cm}.$

Surface area of sphere = 4πr².

Putting values in equation we get,

Surface area of sphere = $4 \times \dfrac{22}{7} \times (3.5)^2$

$= \dfrac{4 \times 22 \times 12.25}{7} \\[1em] = \dfrac{1078}{7} \\[1em] = 154 \text{ cm}^2$

Hence, the radius of the sphere = 3.5 cm and surface area of sphere = 154 cm².