Question

The volume of a hemisphere is $2425\frac{1}{2}c{m}^3$. Find its curved surface area. $[Use\pi =\frac{22}{7}].$

• A. $785.30$ cu. cm
• B. $657.30$ cu. cm
• C. $345.30$ cu. cm
• D. $698.30$ cu. cm

Answer 1

The correct option is D $698.30$ cu. cm

Let the radius of the hemisphere $=$ $r$
Now, Volume of hemisphere $=$ $2425\frac{1}{2}$ cm
$=$ $\frac{4851}{2}$ cm
$\Rightarrow$ $\frac{2}{3}\pi r^3$ $=$ $\frac{4851}{2}$
$\Rightarrow$ $\frac{2}{3}\times \frac{22}{7}\times r^3$ = $\frac{4851}{2}$
$\Rightarrow$ $r^3$ = $\frac{4851\times 21}{88}$
$\Rightarrow$ $r^3=\frac{21}{2}=10.5$ cm
Now, curved surface area $=$ $2\pi r^2$ $=$ $\frac{22}{7}\times 2\times \frac{21}{2}\frac{21}{2}$
$=$ $11\times 3\times 21$
$=$ $693c{m}^2$