Question

कभी कयी हमारे जीवन में पोशाक क्यो अड्चन और बधन बन ज जाते हैं?​

Answer 1

$\large{\mathbb{\colorbox{purple} {\boxed{\boxed{\colorbox{white} {-:Answer:-}}}}}}-:Answer:-</p><p></p><p>\large{ \pmb{ \underline{ \underline{\frak{ \color{peru}{Given::}}}}}}Given::Given::</p><p></p><p>\pink{➠}{ \sf{ \bf{ \frac {dv}{dt}} = \sf1 {cm}^{3}/s \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\:\: \: \: \: \: \: \: ...(i) }}➠dtdv=1cm3/s...(i)</p><p></p><p>\large{ \pmb{ \underline{ \underline{\frak{ \color{pink}{To \: find::}}}}}}Tofind::Tofind::</p><p></p><p>\pink{➠}{ \sf{ Rate \: of \: decrease \: of \: slant \: height.}}➠Rateofdecreaseofslantheight.</p><p></p><p>\large{ \pmb{ \underline{ \underline{\frak{ \color{pin}{Formula \: used::}}}}}}Formulaused::Formulaused::</p><p></p><p>\pink{➠}{ \sf{ Volume_{(cone)}= \frac{1}{3}\pi {r}^{2}h }}➠Volume(cone)=31πr2h</p><p></p><p>\large{ \pmb{ \underline{ \underline{\frak{ \color{plum}{Construction::}}}}}}Construction::Construction::</p><p></p><p>\pink{➠}{ \sf{ Kindly \: refer \: the \: attachment\:also!!}}➠Kindlyrefertheattachmentalso!!</p><p></p><p>\large{ \pmb{ \underline{ \underline{\frak{ \color{blue}{Concept \: required::}}}}}}Conceptrequired::Conceptrequired::</p><p></p><p>\pmb{ \bf{From \: the \: above \: attachment..}}Fromtheaboveattachment..Fromtheaboveattachment..</p><p></p><p>\pink{➠}{ \sf{cos \: {\bf x} =\frac{h}{l} = \frac{ \sqrt{3} }{2} }}➠cosx=lh=23</p><p></p><p>\pink{➠}{ \sf{Radius_{(cone)},(r)= \frac{1}{2} }}➠Radius(cone),(r)=21</p><p></p><p>\pink{➠}{ \sf{Height_{(cone)},(h)= \frac{ \sqrt{3} }{2} l}}➠Height(cone),(h)=23l</p><p></p><p>\large{ \pmb{ \underline{ \underline{\frak{ \color{cyan}{According \: to \: Question::}}}}}}AccordingtoQuestion::AccordingtoQuestion::</p><p></p><p>\pmb{ \bf{Let's \: start \: with \: help \: of \: formulas!!}}Let′sstartwithhelpofformulas!!Let′sstartwithhelpofformulas!!</p><p></p><p>\pink{➠}{ \sf{ Volume_{(cone)}= \frac{1}{3}\pi {r}^{2}h }}➠Volume(cone)=31πr2h</p><p></p><p>{: : \implies{ \sf{ Volume_{(cone)}= \frac{1}{3}\pi { \big( \frac{1}{2} \big)}^{2} \Big( \frac{ \sqrt{3} }{2}l \Big) }}}::⟹Volume(cone)=31π(21)2(23l)</p><p></p><p>{: : \implies{ \sf{ Volume_{(cone)}= \frac{\pi}{8 \sqrt{3} } }}}::⟹Volume(cone)=83π</p><p></p><p>\pink{➠}{ \sf{ \bf{ \frac {dv}{dt}} = \sf1 {cm}^{3}/s \: \: \: \: \: \: \:\{ from \: eq. \: ..(i) \}}}➠dtdv=1cm3/s{fromeq...(i)}</p><p></p><p>: : \implies{ \sf{ \bf{ \frac {d}{dt}}} \Big[\frac{\pi}{8 \sqrt{3}} {l}^{3} \Big ] = \sf1 {cm}^{3}/s }::⟹dtd[83πl3]=1cm3/s</p><p></p><p>: : \implies{ \sf \frac{\pi}{8 \sqrt{3}} { \bf{ \frac {d}{dt}}}{(l)}^{3} = \sf1 {cm}^{3}/s }::⟹83πdtd(l)3=1cm3/s</p><p></p><p>: : \implies{ \sf \frac{3 {l}^{2}\pi }{8 \sqrt{3}} { \bf{ \frac {d}{dt}}} = \sf1 {cm}^{3}/s }::⟹833l2πdtd=1cm3/s</p><p></p><p>{: : \implies{ \sf \frac{ \sqrt{3} (16\pi )}{8 } { \bf{ \frac {dl}{dt}}} = \sf1 {cm}^{3}/s \: \: \: \: \: \: \: \: \{∵At \: l=4cm \}}}::⟹83(16π)dtdl=1cm3/s{∵Atl=4cm}</p><p></p><p>{: : \implies{ \sf2 \sqrt{3} \pi { \bf{ \frac {dl}{dt}}} = \sf1 {cm}^{3}/s}}::⟹23πdtdl=1cm3/s</p><p></p><p>{: : \implies{ \sf{ \bf{ \frac {dl}{dt}}} = \sf \: \frac{1}{2 \sqrt{3}\pi } {cm}^{3}/s}}::⟹dtdl=23π1cm3/s</p><p></p><p>\pmb {\bf{Hence,}}Hence,Hence,</p><p></p><p>\purple᪣ {\boxed{ \sf{ Rate \: of \: decrease \: of \: slant \: height = \frac{1}{2 \sqrt{3} {\pi}}{cm}^{3} /s }}} ᪣᪣Rateofdecreaseofslantheight=23π1cm3/s᪣</p><p></p><p>ᚚᚚᚚᚚᚚᚚᚚᚚᚚᚚᚚᚚᚚᚚᚚᚚᚚᚚᚚᚚᚚᚚᚚᚚᚚᚚᚚᚚᚚᚚᚚᚚᚚᚚᚚᚚ</p><p></p><p>$