Question

The volume of a hemisphere is $2425\frac{1}{2}c{m}^3.$ Find its curved surface area.

Answer 1

As, volume of hemisphere $=2425\frac{1}{2}c{m}^3$

$\Rightarrow \frac{2}{3}\pi r^3=2425\frac{1}{2}$ [$\because$ Volume of the hemisphere $=\frac{2}{3}\pi r^3$]

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

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

$\Rightarrow r^3=\frac{441\times 3\times 7}{2\times 2\times 2}$

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

$\Rightarrow r=\frac{21}{2}cm$
So, the curved surface area of the hemisphere $=2\pi r^2=2\times \frac{22}{7}\times \frac{21}{2}\times \frac{21}{2}=693c{m}^2$