Question

Q#4. A hemisphere has a curved surface area of 364.531cm 2 . Find its
radius.

Answer 1

$\large\bf\underline{Given:-}$

• CSA of hemisphere = 364.531cm²

$\large\bf\underline {To \: find:-}$

• Radius of hemisphere

$\huge\bf\underline{Solution:-}$

$\mid \underline {\boxed{ \bf \:CSA of Hemisphere = 2 \pi {r}^{2} }} \mid$

CSA of Hemisphere = 364.531cm²

↣2πr² = 364.531

↣2 × 22/7 × r² = 364.531

↣ 44/7 × r² = 364.531

↣r² = 364.531 × 7/44

↣r² = 2551.717/44

↣r² = 58

↣r = √58

↣r = 7.6cm

Hence,

▶️ Radius of Hemisphere = 7.6cm.

$\rule{200}3$

Some formula's :-

»★CSA of hemisphere = 2πr²

»★ TSA of Hemisphere = 3πr²

»★ Volume of Hemisphere = ⅔πr²

where,

• CSA = Curved surface area
• TSA = Total Surface area

$\rule{200}3$

Answer 2

Answer:-

$\sf{The \ radius \ of \ the \ hemisphere \ is \ 7.6 \ cm}$

Given:

• For hemisphere,
• $\sf{Curved \ surface \ area=364.531}$

To find:

• The radius of the hemisphere.

Solution:

$\boxed{\sf{Curved \ surface \ area \ of \ hemisphere=2\times\pi\times \ r^{2}}}$

$\sf{\therefore{2\times\pi\times \ r^{2}=364.531}}$

$\sf{\therefore{r^{2}=\frac{364.531\times7}{2\times22}}}$

$\sf{\therefore{r^{2}=\frac{2551.717}{44}}}$

$\sf{\therefore{r^{2}=57.99 (approx)}}$

$\sf{On \ taking \ square \ root \ of \ both \ sides}$

$\sf{r=7.6 \ cm \ (approx)}$

$\sf\purple{\tt{\therefore{The \ radius \ of \ the \ hemisphere \ is \ 7.6 \ cm}}}$