Question

If the volume of a hemisphere is 18π cm³, then its total surface area is __________.

Answer 1

Let r be the radius of the hemisphere.

Volume of the hemisphere = 18$\mathrm{\pi }$ cm³ (Given)

$\Rightarrow \frac{2}{3}\mathrm{\pi }{r}^3=18\mathrm{\pi }$

$\Rightarrow r^3=\frac{18\times 3}{2}=27$

$\Rightarrow r^3={\left(3\right)}^3$

$\Rightarrow r=3\mathrm{cm}$

∴ Total surface area of the hemisphere

= 3$\mathrm{\pi }$r²

= 3$\mathrm{\pi }$× (3 cm)²

= 27$\mathrm{\pi }$ cm²

Thus, the total surface area of the hemisphere is 27$\mathrm{\pi }$ cm².

If the volume of a hemisphere is 18π cm³, then its total surface area is ___27$\mathrm{\pi }$ cm²___.