The volume of a hemi-sphere is $2425 \frac{1}{2} \mathrm{~cm}^{3}$. Find its curved surface area. (Use $\pi=22 / 7$ )
Let the radius of the hemisphere be r cm.
Volume of hemisphere $=2425 \frac{1}{2} \mathrm{~cm}^{3}$
$\Rightarrow \frac{2}{3} \pi r^{3}=\frac{4851}{2}$
$\Rightarrow \frac{2}{3} \times \frac{22}{7} r^{3}=\frac{4851}{2}$
$\Rightarrow r^{3}=\frac{4851 \times 3 \times 7}{2 \times 2 \times 22}$
$\Rightarrow r^{3}=\frac{441 \times 21}{2 \times 2 \times 2}$
$\Rightarrow r^{3}=\left(\frac{21}{2}\right)^{3}$
$\Rightarrow r=\frac{21}{2} \mathrm{~cm}$
Now, the curved surface area of hemisphere is given by
$2 \pi r^{2}$
$=2 \times \frac{22}{7} \times\left(\frac{21}{2}\right)^{2}$
$=693 \mathrm{~cm}^{2}$
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