Question

curved surface area of a hemisphere is77 cm^2 . Then the radius of hemisphere is
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Answer 1

★ Given : Curved surface area of a hemisphere is77 cm² .

$\rule{130}1$

★ Solution :

Let the radius of hemisphere be r cm.

☯ $\underline{\boldsymbol{According\: to \:the\: Question\:now :}}$

$:\implies\sf CSA\:of\: Hemisphere = 2 \pi r^2 \\\\\\:\implies\sf 2\pi r^2 = 77 \\\\\\:\implies\sf 2 \times \dfrac{22}{7} \times r^2 = 77\\\\\\:\implies\sf r^2 = \dfrac{77 \times 7}{2 \times 22}\\\\\\:\implies\sf r^2 = \dfrac{49}{21}\\\\\\:\implies\sf r = \sqrt{\dfrac{49}{21}} \\\\\\:\implies\sf r = \dfrac{7}{2}\\\\\\:\implies\underline{\boxed {\sf Radius = 3.5\:cm}}$

⠀

$\therefore\:\underline{\textsf{The radius of hemisphere is \textbf{3.5 cm}}}.$

$\rule{170}2$

Answer 2

GIVEN:

• CSA of Hemisphere = 77 cm²

TO FIND:

• What is the radius of Hemisphere ?

SOLUTION:

Let the radius of Hemisphere be 'r' cm

To find the CSA of Hemisphere, we use the formula:-

$\large{\boxed{\bf{\star \: CSA = 2 \pi r^2 \: \star}}}$

According to question:-

➸ 77 = 2 $\times$ $\sf{\dfrac{22}{7}}$ $\times$ r²

➸ 77 = $\sf{\dfrac{44}{7}}$ $\times$ r²

➸ $\sf{\dfrac{77 \times 7}{44}}$ = r²

➸ $\sf{\cancel\dfrac{539}{44}}$ = r²

➸ $\sf{\dfrac{49}{4}}$ = r²

➸ $\sf{ \sqrt{\dfrac{49}{4}}}$ = r

❮ $\bf{\dfrac{7}{2}}$ cm = r ❯

❝ Hence, the radius of Hemisphere is 7/2 cm ❞

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