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 $=3 \pi r^{2}$
$=\left(3 \times \frac{22}{7} \times 21 \times 21\right) \mathrm{cm}^{2}$
$=4158 \mathrm{~cm}^{2}$
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