If the total surface area of a hemisphere is \(462\text{cm}^2\) , calculate its radius.

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

Given,
$3\pi r^2 = 462$

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

$3 \times \frac{22}{7} \times r^2 = 462$

$\frac{66}{7} r^2 = 462$

Multiply both sides by 7:

$66r^2 = 462 \times 7$

$66r^2 = 3234$

$r^2 = 49$

r = 7 cm

Answer: The radius is 7 cm.