The volume of a hemisphere is $2425\dfrac{1}{2}$ cm³. Find its curved surface area.

Let radius of hemisphere be r cm.

Volume of hemisphere (V) = $\dfrac{2}{3}πr^3$

Given, V = $2425\dfrac{1}{2} = \dfrac{4851}{2}$.

$\therefore \dfrac{2}{3} \times \dfrac{22}{7} \times r^3 = \dfrac{4851}{2} \\[1em] \Rightarrow r^3 = \dfrac{4851 \times 3 \times 7}{2 \times 22 \times 2} \\[1em] \Rightarrow r^3 = \dfrac{441 \times 3 \times 7}{2 \times 2 \times 2} \\[1em] \Rightarrow r^3 = \dfrac{9261}{8} \\[1em] \Rightarrow r^3 = \Big(\dfrac{21}{2}\Big)^3 \\[1em] \Rightarrow r = \dfrac{21}{2} \text{ cm}.$

Curved surface area = 2πr²

$= 2 \times \dfrac{22}{7} \times \dfrac{21}{2} \times \dfrac{21}{2} \\[1em] = \dfrac{44 \times 441}{28} \\[1em] = 693 \text{ cm}^2.$

Hence, curved surface area of hemisphere = 693 cm².