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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Updated on: 10-Oct-2022

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