Question

total surface of hemisphere is 942cm2 find its volume( take pi=22/7)​

Answer 1

$\large{ \bold{ \star{ \underline{ \underline{ \red{ \mathrm{Question...}}}}}}}$

$\large{ \mathrm{ \bullet{ \: \: total \: surface \: area \: of \: hemispheres \: is \: 942cm {}^{2} .}}} \\ \large{ \mathrm{find \: its \: volume....{\pi = \frac{22}{7} }}}$

$\large{ \star{ \mathrm{ \underline{ \underline{ \red{Answer...}}}}}}$

$\large{ \mathrm{ \pink{volume = \frac{4312 \sqrt{2} }{2} cm {}^{3} }}}$

$\large{ \mathrm{ \star{ \underline{ \underline{ \red{ Solution...}}}}}}$

$\large{ \purple{ \mathrm{ \mapsto{we \: know \: that...}}}} \\ \\ \large{ \mathrm{total \: surface \: area \: of \: hemisphere}} \\ \large{ \boxed{ \green {= 3\pi {r}^{2} }}} \: \large{ \red{ \mathrm{here \: r = radius \: }}} \\ \\ : \large{ \mathrm{ \implies{3\pi {r}^{2} = 942 \: cm {}^{2} }}} \\ \\ : \large{ \mathrm{ \implies{3 \times \frac{22}{7} \times {r}^{2} = 942cm {}^{2} }}} \\ \\ : \large{ \mathrm{ \implies{ {r}^{2} = \frac{ 14\: \: \cancel{42} \: \: \cancel{942 } \times 7}{ \cancel{22} \times \cancel{ 3}} }}} \\ \\ : \large{ \mathrm{ \implies{ {r}^{2} = 2 \times 7 \times 7 \: cm {}^{2} }}} \\ \\ : \large{ \mathrm{ \implies{ \boxed{ \red{r = 7 \sqrt{2} cm}}}}}$

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

$\large{ \mathrm{ \purple{ \mapsto{we \: must \: know...}}}} \\ \\ \large{ \mathrm{volume \: of \: hemisphere}} \\ \large{ \boxed{ \red{ = \frac{2}{3} \pi {r}^{2} }}} \\ \\ \large{ \mathrm{ \green{we \: have \: r = 7 \sqrt{2} cm}}} \\ \\ : \large{ \mathrm{ \implies{ \frac{2}{3} \times \frac{22}{ \cancel{7}} \times \cancel{7} \sqrt{2} cm \times 7 \sqrt{2} cm \times 7 \sqrt{2} cm}}} \\ \\ : \large{ \mathrm{ \implies{ \frac{2 \times 22 \times 7 \times 7 \times 2 \sqrt{2} }{3} cm {}^{3} }}} \\ \\ : \large{ \mathrm{ \implies{ \boxed{ \red{ \frac{4312 \sqrt{2} }{3} cm {}^{3} }}}}} \\ \\ \large{ \therefore{ \mathrm{ \underline{ \underline{ \green{volume \: of \: hemisphere = \frac{4312 \sqrt{2} }{3} cm {}^{3} }}}}}}$

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━