Question

If the total surface area of a solid hemisphere is 462 $c{m}^2$, find its volume.
[Take $\pi =\frac{22}{7}]$

Answer 1

Total surface area of hemisphere = $3\pi r^2$ = $462c{m}^2$ (given)
$⟹\frac{3\times 22}{7}\times r^2=462$
$⟹r^2=\frac{462\times 7}{3\times 22}$

$⟹r^2=49$
$⟹r=7cm$
Volume of hemisphere $=\frac{2}{3}\pi r^3$
$=\frac{2}{3}\times \frac{22}{7}\times 7^3$

$=\frac{2156}{3}$ $c{m}^3$

$=718.67c{m}^3$