Question

if the circumference of the base of cylinder is
44cm and the sum of its radius and height is
27 cm, find its total surface area.


​

Answer 1

$\sf Given \begin{cases} & \sf{Circumference\:of\:the\:base\;of\:cylinder = \bf{44\:cm}} \\ & \sf{Sum\:of\:radius\:and\:height\:of\:cylinder = \bf{27\:cm}} \end{cases}$

To find: Total surface area of cylinder?

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☯ Let's consider r and h be the radius and height of cylinder respectively.

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$\dag\;{\underline{\frak{As\;we\;know\;that,}}}$

$\star\;{\boxed{\sf{\pink{Circumference_{\;(circle)} = 2 \pi r}}}}$

$:\implies\sf 2 \times \dfrac{22}{7} \times r = 44$

$:\implies\sf \dfrac{44}{7} \times r = 44$

$:\implies\sf r = \cancel{44} \times \dfrac{7}{ \cancel{44}}$

$:\implies{\underline{\boxed{\frak{\purple{r = 7\:cm}}}}}\;\bigstar$

$\therefore\:{\underline{\sf{Radius\:of\:cylinder\:is\: {\textsf{\textbf{7\:cm}}}.}}}$

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$\underline{\bigstar\:\boldsymbol{According\:to\:the\:question\::}}$

Sum of radius and height of cylinder is 27 cm.

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$:\implies\sf r + h = 27$

$:\implies\sf 7 + h = 27$

$:\implies\sf h = 27 - 7$

$:\implies{\underline{\boxed{\frak{\purple{h = 20\:cm}}}}}\;\bigstar$

$\therefore\:{\underline{\sf{Height\:of\:cylinder\:is\: {\textsf{\textbf{20\:cm}}}.}}}$

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☯ Now, Finding Curved surface area of cylinder,

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$\star\;{\boxed{\sf{\pink{Total\:surface\:area_{\;(rectangle)} = 2 \pi r(r + h)}}}}$

$:\implies\sf 2 \times \dfrac{22}{ \cancel{7}} \times \cancel{7} \bigg( 7 + 20 \bigg)$

$:\implies\sf 2 \times 22 \times 27$

$:\implies{\underline{\boxed{\frak{\purple{1188\:cm^2}}}}}\;\bigstar$

$\therefore\:{\underline{\sf{Total\:surface\:area\:of\:cylinder\:is\: \bf{1188\:cm^2}.}}}$

Answer 2

Answer:

$\sf Given \begin{cases} & \sf{Circumference\:of\:the\:base\;of\:cylinder = \bf{44\:cm}} \\ & \sf{Sum\:of\:radius\:and\:height\:of\:cylinder = \bf{27\:cm}} \end{cases}$

To find: Total surface area of cylinder?

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀

☯ Let's consider r and h be the radius and height of cylinder respectively.

⠀⠀⠀⠀

$\dag\;{\underline{\frak{As\;we\;know\;that,}}}$

$\star\;{\boxed{\sf{\pink{Circumference_{\;(circle)} = 2 \pi r}}}}$

$:\implies\sf 2 \times \dfrac{22}{7} \times r = 44$

$:\implies\sf \dfrac{44}{7} \times r = 44$

$:\implies\sf r = \cancel{44} \times \dfrac{7}{ \cancel{44}}$

$:\implies{\underline{\boxed{\frak{\purple{r = 7\:cm}}}}}\;\bigstar$

$\therefore\:{\underline{\sf{Radius\:of\:cylinder\:is\: {\textsf{\textbf{7\:cm}}}.}}}$

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀

$\underline{\bigstar\:\boldsymbol{According\:to\:the\:question\::}}$

Sum of radius and height of cylinder is 27 cm.

⠀⠀⠀⠀

$:\implies\sf r + h = 27$

$:\implies\sf 7 + h = 27$

$:\implies\sf h = 27 - 7$

$:\implies{\underline{\boxed{\frak{\purple{h = 20\:cm}}}}}\;\bigstar$

$\therefore\:{\underline{\sf{Height\:of\:cylinder\:is\: {\textsf{\textbf{20\:cm}}}.}}}$

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☯ Now, Finding Curved surface area of cylinder,

⠀⠀⠀

$\star\;{\boxed{\sf{\pink{Total\:surface\:area_{\;(rectangle)} = 2 \pi r(r + h)}}}}$

$:\implies\sf 2 \times \dfrac{22}{ \cancel{7}} \times \cancel{7} \bigg( 7 + 20 \bigg)$

$:\implies\sf 2 \times 22 \times 27$

$:\implies{\underline{\boxed{\frak{\purple{1188\:cm^2}}}}}\;\bigstar$

$\therefore\:{\underline{\sf{Total\:surface\:area\:of\:cylinder\:is\: \bf{1188\:cm^2}.}}}$