The volume of a solid hemisphere is \(\frac{396}{7}\text{cm}^3\). Find the total surface area of hemisphere

Volume of hemisphere
$V = \frac{2}{3}\pi r^3$

Given,
$\frac{2}{3}\pi r^3 = \frac{396}{7}$

Using $\pi = \frac{22}{7}$,

$\frac{2}{3} \times \frac{22}{7} \times r^3 = \frac{396}{7}$

$\frac{44}{21} r^3 = \frac{396}{7}$

Multiply both sides by 21:

$44r^3 = 396 \times 3$

$44r^3 = 1188$

$r^3 = 27$

$r = 3$ cm

Total surface area of hemisphere
$= 3\pi r^2$

$= 3 \times \frac{22}{7} \times 9$

$= \frac{594}{7} \approx 84.85 \text{ cm}^2$

Correct option: $84.85 \text{ cm}^2$