The volume of a hemisphere is 19404 cm3.
Question:

The volume of a hemisphere is 19404 cm3. The total surface area of the hemisphere is
(a) 4158 cm2
(b) 16632 cm2
(c) 8316 cm2
(d) 3696 cm2

Solution:

(a) 4158 cm2

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

Therefore,

$\frac{2}{3} \pi r^{3}=19404$

$\Rightarrow \frac{2}{3} \times \frac{22}{7} \times r^{3}=19404$

$\Rightarrow r^{3}=\left(19404 \times \frac{21}{44}\right)$

$\Rightarrow r^{3}=(21)^{3}$

$\Rightarrow r=21 \mathrm{~cm}$

Hence, the total surface area of the hemisphere $=3 \pi r^{2}$

$=\left(3 \times \frac{22}{7} \times 21 \times 21\right) \mathrm{cm}^{2}$

$=4158 \mathrm{~cm}^{2}$