The volume of a hemi-sphere is $ 2425 \frac{1}{2} \mathrm{~cm}^{3} $. Find its curved surface area. (Use $ \pi=22 / 7 $ )

Given:

The volume of a hemi-sphere is \( 2425 \frac{1}{2} \mathrm{~cm}^{3} \).

To do:

We have to find its curved surface area.

Solution:

Volume of the hemisphere $=2425 \frac{1}{2} \mathrm{~cm}^{3}$

$=\frac{4851}{2} \mathrm{~cm}^{3}$

Let $r$ be the radius of the hemisphere.

Therefore,

Volume of the hemisphere $=\frac{1}{2} \times \frac{4}{3} \pi r^{3}$

$\Rightarrow \frac{2}{3} \times \frac{22}{7} r^{3}=\frac{4851}{2}$

$\Rightarrow r^{3}=\frac{4851}{2} \times \frac{3 \times 7}{2 \times 22}$

$\Rightarrow r^{3}=\frac{441 \times 21}{2 \times 2 \times 2}$

$\Rightarrow r^{3}=\frac{21 \times 21 \times 21}{2 \times 2 \times 2}$

$\Rightarrow r^{3}=(\frac{21}{2})^{3}$

$\Rightarrow r=\frac{21}{2} \mathrm{~cm}$

Curved surface area of the hemisphere $=2 \pi r^{2}$

$=2 \times \frac{22}{7} \times(\frac{21}{2})^{2}$

$=\frac{2 \times 22 \times 21 \times 21}{7 \times 2 \times 2}$

$=693 \mathrm{~cm}^{2}$

The curved surface area of the hemisphere is $693\ cm^2$.

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Updated on: 10-Oct-2022

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