Question

If the total surface area of a solid hemisphere is $462c{m}^2$, find its volume.

Answer 1

TSA of a hemisphere $=3\pi r^2$

$\Rightarrow 3\pi r^2=462c{m}^2$

$\Rightarrow 3\times \frac{22}{7}\times r^2=462c{m}^2$

$\Rightarrow r^2=462\times \frac{7}{22}\times \frac{1}{3}c{m}^2$

$\Rightarrow r^2=7\times 7c{m}^2$

$\Rightarrow r=7cm$
Volume of hemisphere $=\frac{2}{3}\pi r^3$

$=\frac{2}{3}\times \frac{22}{7}\times (7cm{)}^3$

$=\frac{2}{3}\times \frac{22}{7}\times 7cm\times 7cm\times 7cm$
$=718.67c{m}^3$ (Approximately)