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If the total surface area of a solid hemisphere is $ 462 \mathrm{~cm}^{2} $, find its volume (Take $ \pi=22 / 7 $ )
Given:
The total surface area of the solid hemisphere is \( 462 \mathrm{~cm}^{2} \).
To do:
We have to find the volume of the solid hemisphere.
Solution:
Total surface area of the solid hemisphere $=462 \mathrm{~cm}^{2}$
Let $r$ be the radius of the hemisphere.
Therefore,
Total surface area of the cylinder $=3 \pi r^{2}$
$3 \pi r^{2}=462$
$\Rightarrow \frac{3 \times 22}{7} r^{2}=462$
$\Rightarrow r^{2}=\frac{462 \times 7}{3 \times 22}$
$\Rightarrow r^{2}=49$
$\Rightarrow r^{2}=(7)^{2}$
$\Rightarrow r=7 \mathrm{~cm}$
Volume of the solid hemisphere $=\frac{2}{3} \pi r^{3}$
$=\frac{2}{3} \times \frac{22}{7} \times 7^3$
$=\frac{2156}{3}$
$=718 \frac{2}{3} \mathrm{~cm}^{3}$
The volume of the solid hemisphere is $718 \frac{2}{3} \mathrm{~cm}^{3}$.
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