The curved surface area of a hemisphere is 693 cm². What is the volume of the hemisphere?

Let r be the radius of the hemisphere.

The curved surface area of the hemisphere = 2πr²

$\therefore 2{\mathrm{\pi r}}^2=693$

$\Rightarrow 2\times \frac{22}{7}\times {\mathrm{r}}^2=693$

$\Rightarrow {\mathrm{r}}^2=\frac{693\times 7}{2\times 22}=\frac{3\times 3\times 7\times 7}{2\times 2}$

$\Rightarrow \mathrm{r}=\frac{21}{2} \mathrm{cm}$

∴ The volume of the hemisphere  = $\frac{2}{3}{\mathrm{\pi r}}^3=\frac{2}{3}\times \frac{22}{7}\times {\left(\frac{21}{2}\right)}^3=2425.5 {\mathrm{cm}}^3$

Thus, the volume of the hemisphere is 2425.5 cm³.