Lateral surface area of hollow cylinder

Asked by admin @ 10/08/2021 in Math viewed by 313 People

12. The lateral surface area of a hollow cylinder is 6600 m2. It is cut along its height and formed a rectangular sheet of width 30 m.

Find the perimeter of rectangular sheet.

Answered by admin @ 10/08/2021

$\sf \bf \huge {\boxed {\mathbb {QUESTION}}}$

$\tt The\: lateral\: surface\: area\: of\: a\: hollow\: cylinder\\\tt is\: 6600\: {m}^{2}. \:It\: is\: cut\: along\: its\: height\: and\\\tt formed\: a\: rectangular \:sheet \:of \:width \:30 m\:. \\\tt Find\: the\: perimeter \:of \:rectangular\: sheet.$

$\sf \bf \huge {\boxed {\mathbb {ANSWER}}}$

$\sf \bf {\boxed {\mathbb {GIVEN}}}$

$\sf \bf L.S.A \:of\:hollow\:cylinder =6600\: {m}^{2}$
$\sf \bf Width=30m$

$\sf \bf {\boxed {\mathbb {TO\:FIND}}}$

$\sf \bf Perimeter \:of\:the\:rectangular\:sheet$

$\sf \bf {\boxed {\mathbb {SOLUTION}}}$

$\tt \underline {Area \:of \:cylinder \:and \:sheet \:are\:same}$

$\\$

$\sf \bf (C.S.A\:of\:cylinder) =(Area\:of\:sheet)$

$\sf \bf \implies 6600=l \times b$

$\sf \bf \implies 6600=l \times 30$

$\sf \bf \implies l= \dfrac{660\cancel {0}} {3\cancel {0}}$

$\sf \bf \implies l=\dfrac{660}{3}$

$\implies {\boxed {\color {green} {\sf \bf l=220\: {m}^{2}}}}$

-----------------------------------------------------------

${\boxed {\boxed {\color {blue} {\sf \bf P=2(l+b)}}}}$

$\sf \bf P=perimeter\:of\:rectangle$
$\sf \bf l=length$
$\sf \bf b=breadth$

$\\$

${\overbrace {\underbrace {\color {orange} {\sf \bf Substitute \:the\:values}}}}$

$\\$

$\sf \bf \implies P=2(220 + 30)$

$\sf \bf \implies P=2(250)$

$\implies {\boxed {\boxed {\color {red} {\sf \bf P=500\:m}}}}$

$\tt {\color {purple} { \therefore The\:primeter\:of\:rectangular \:sheet \:is=550\:m}}$

$\sf \bf \huge {\boxed {\mathbb {HOPE \:IT \:HELPS \:YOU}}}$

_________________________________________

$\sf \bf \huge {\boxed {\mathbb {EXTRA\:INFORMATION}}}$

$\sf \bf L.S.A\:of\:cylinder =2 \pi r h$

$\sf \bf T.S.A\:of\:cylinder =2 \pi r(r+h)$

$\sf \bf Volume\:of\:cylinder =\pi {r}^{2} h$

${\mathbb{\colorbox {orange} {\boxed{\boxed{\boxed{\boxed{\boxed{\colorbox {lime} {\boxed{\boxed{\boxed{\boxed{\boxed{\colorbox {aqua} {@suraj5070}}}}}}}}}}}}}}}$

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