The volume of a hemi-sphere is

Question:

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

Solution:

Let the radius of the hemisphere be 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

$2 \pi r^{2}$

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

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