Question Number 82591 by Learner-123 last updated on 22/Feb/20 | ||
$${A}\:{closed}\:{surface}\:{is}\:{defined}\:{in}\:{spherical} \\ $$ $${coordinates}\:{by}\:\mathrm{3}<{r}<\mathrm{5}\:,\:\mathrm{0}.\mathrm{1}\pi<\theta<\mathrm{0}.\mathrm{3}\pi, \\ $$ $$\mathrm{1}.\mathrm{2}\pi<\phi<\mathrm{1}.\mathrm{6}\pi.\:\boldsymbol{{F}}{ind}\:{the}\:{total}\:{surface} \\ $$ $${area}. \\ $$ | ||
Commented byLearner-123 last updated on 22/Feb/20 | ||
$${Ans}:\mathrm{36}.\mathrm{79}\:{square}\:{units}. \\ $$ | ||
Commented byLearner-123 last updated on 23/Feb/20 | ||
Commented byLearner-123 last updated on 23/Feb/20 | ||
$${Sir},\:{this}\:{is}\:{the}\:{explaination}\:{given}. \\ $$ $${Can}\:{you}\:{tell}\:{how}\:{these}\:\mathrm{4}\:\left({actually}\:\mathrm{5}\right){terms} \\ $$ $${come}.. \\ $$ | ||
Commented bymr W last updated on 23/Feb/20 | ||
Commented bymr W last updated on 23/Feb/20 | ||
$${in}\:{our}\:{case} \\ $$ $$\phi=\mathrm{0}.\mathrm{1}\pi..\mathrm{0}.\mathrm{3}\pi \\ $$ $$\theta=\mathrm{1}.\mathrm{2}\pi..\mathrm{1}.\mathrm{6}\pi \\ $$ $${r}=\mathrm{3}..\mathrm{5} \\ $$ $${we}\:{have}\:{totally}\:\mathrm{6}\:{faces}: \\ $$ $${face}\:\mathrm{1}:\:{r}=\mathrm{3},\:\phi=\mathrm{0}.\mathrm{1}\pi...\mathrm{0}.\mathrm{3}\pi,\:\theta=\mathrm{1}.\mathrm{2}\pi..\mathrm{1}.\mathrm{6}\pi \\ $$ $${A}_{\mathrm{1}} =\int_{\mathrm{1}.\mathrm{2}\pi} ^{\mathrm{1}.\mathrm{6}\pi} \int_{\mathrm{0}.\mathrm{1}\pi} ^{\mathrm{0}.\mathrm{3}\pi} {r}\:\mathrm{sin}\:\theta\:{d}\phi{rd}\theta=\mathrm{3}^{\mathrm{2}} \int_{\mathrm{1}.\mathrm{2}\pi} ^{\mathrm{1}.\mathrm{6}\pi} \int_{\mathrm{0}.\mathrm{1}\pi} ^{\mathrm{0}.\mathrm{3}\pi} \mathrm{sin}\:\theta\:{d}\phi{d}\theta \\ $$ $${face}\:\mathrm{2}:\:{r}=\mathrm{5},\:\phi=\mathrm{0}.\mathrm{1}\pi...\mathrm{0}.\mathrm{3}\pi,\:\theta=\mathrm{1}.\mathrm{2}\pi..\mathrm{1}.\mathrm{6}\pi \\ $$ $${A}_{\mathrm{2}} ={similarly}=\mathrm{5}^{\mathrm{2}} \int_{\mathrm{1}.\mathrm{2}\pi} ^{\mathrm{1}.\mathrm{6}\pi} \int_{\mathrm{0}.\mathrm{1}\pi} ^{\mathrm{0}.\mathrm{3}\pi} \mathrm{sin}\:\theta\:{d}\phi{d}\theta \\ $$ $${face}\:\mathrm{3}:\:\phi=\mathrm{0}.\mathrm{1}\pi,\:\theta=\mathrm{1}.\mathrm{2}\pi..\mathrm{1}.\mathrm{6}\pi,\:{r}=\mathrm{3}..\mathrm{5} \\ $$ $${A}_{\mathrm{3}} =\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{5}^{\mathrm{2}} −\mathrm{3}^{\mathrm{2}} \right)\left(\mathrm{1}.\mathrm{6}\pi−\mathrm{1}.\mathrm{2}\pi\right) \\ $$ $${face}\:\mathrm{4}:\:\phi=\mathrm{0}.\mathrm{3}\pi,\:\theta=\mathrm{1}.\mathrm{2}\pi..\mathrm{1}.\mathrm{6}\pi,\:{r}=\mathrm{3}..\mathrm{5} \\ $$ $${A}_{\mathrm{4}} =\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{5}^{\mathrm{2}} −\mathrm{3}^{\mathrm{2}} \right)\left(\mathrm{1}.\mathrm{6}\pi−\mathrm{1}.\mathrm{2}\pi\right) \\ $$ $${face}\:\mathrm{5}:\:\phi=\mathrm{0}.\mathrm{1}\pi..\mathrm{0}.\mathrm{3}\pi,\:\theta=\mathrm{1}.\mathrm{2}\pi,\:{r}=\mathrm{3}..\mathrm{5} \\ $$ $${A}_{\mathrm{5}} =\int_{\mathrm{0}.\mathrm{1}\pi} ^{\mathrm{0}.\mathrm{3}\pi} \int_{\mathrm{3}} ^{\mathrm{5}} \mathrm{sin}\:\mathrm{1}.\mathrm{2}\pi\:{d}\phi{rdr} \\ $$ $${face}\:\mathrm{6}:\:\phi=\mathrm{0}.\mathrm{1}\pi..\mathrm{0}.\mathrm{3}\pi,\:\theta=\mathrm{1}.\mathrm{6}\pi,\:{r}=\mathrm{3}..\mathrm{5} \\ $$ $${A}_{\mathrm{6}} =\int_{\mathrm{0}.\mathrm{1}\pi} ^{\mathrm{0}.\mathrm{3}\pi} \int_{\mathrm{3}} ^{\mathrm{5}} \mathrm{sin}\:\mathrm{1}.\mathrm{6}\pi\:{d}\phi{rdr} \\ $$ $${A}=\Sigma{A} \\ $$ $$=\left(\mathrm{3}^{\mathrm{2}} +\mathrm{5}^{\mathrm{2}} \right)\int_{\mathrm{1}.\mathrm{2}\pi} ^{\mathrm{1}.\mathrm{6}\pi} \int_{\mathrm{0}.\mathrm{1}\pi} ^{\mathrm{0}.\mathrm{3}\pi} \mathrm{sin}\:\theta\:{d}\phi{d}\theta \\ $$ $$+\mathrm{2}×\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{5}^{\mathrm{2}} −\mathrm{3}^{\mathrm{2}} \right)\left(\mathrm{1}.\mathrm{6}\pi−\mathrm{1}.\mathrm{2}\pi\right) \\ $$ $$+\left(\mathrm{sin}\:\mathrm{1}.\mathrm{2}\pi+\mathrm{sin}\:\mathrm{1}.\mathrm{6}\pi\right)\left(\mathrm{0}.\mathrm{3}\pi−\mathrm{0}.\mathrm{1}\pi\right)\int_{\mathrm{3}} ^{\mathrm{5}} {rd}\phi{dr} \\ $$ | ||
Commented byLearner-123 last updated on 24/Feb/20 | ||
$${Thank}\:{You}\:{Sir}! \\ $$ $${Can}\:{you}\:{please}\:{solve}\:{my}\:{other}\:\mathrm{3}\:{doubts}? \\ $$ | ||
Commented bymr W last updated on 24/Feb/20 | ||
$${i}\:{don}'{t}\:{know}\:{what}\:{are}\:{your}\:{doubts}.\:{you} \\ $$ $${should}\:{not}\:{assume}\:{that}\:{i}\:{know}\:{all}\:{posts}. \\ $$ | ||
Commented byLearner-123 last updated on 24/Feb/20 | ||
$${Question}\:{no}:\:\mathrm{82627}\:,\:\mathrm{82631},\mathrm{82647} \\ $$ | ||
Commented byLearner-123 last updated on 24/Feb/20 | ||
$${I}\:{think}\:{there}\:{is}\:{some}\:{technical}\:{problem} \\ $$ $${in}\:{this}\:{app},\:{whenever}\:{i}\:{press}\:\natural\boldsymbol{{s}}{ort}\:{by} \\ $$ $${recent}\:{activity}\varepsilon\:{it}\:{gets}\:{me}\:{to}\:{same} \\ $$ $${integral}\:{question}\:{everytime}...\left(\mathrm{75986}\right) \\ $$ | ||
Commented bymr W last updated on 24/Feb/20 | ||
$${i}\:{can}'{t}\:{help}\:{you}. \\ $$ | ||
Commented bymr W last updated on 26/Feb/20 | ||
$${both} \\ $$ | ||
Commented byLearner-123 last updated on 26/Feb/20 | ||
$${Are}\:{you}\:{referring}\:{to}\:{my}\:{doubt}\:{or} \\ $$ $${this}\:{technical}\:{glitch}? \\ $$ | ||