Question

The radius of the cylinder is 7 cm is it volume is 2002 cm then find (i) if height (ii) total surface area

Answer 1

height=13cm
total surface area=880cm

Answer 2

$\sf Given \begin{cases} & \sf{Radius\:of\:cylinder = \bf{7\:cm}} \\ & \sf{Volume\:of\:cylinder = \bf{2002\:cm^3}} \end{cases}$

To find: Height and TSA of cylinder?

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☯ Let height of cylinder be h cm.

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$\setlength{\unitlength}{1.1mm}\begin{picture}(5,5)\thicklines\multiput(-0.5,-1)(26,0){2}{\line(0,1){40}}\multiput(12.5,-1)(0,3.2){13}{\line(0,1){1.6}}\multiput(12.5,-1)(0,40){2}{\multiput(0,0)(2,0){7}{\line(1,0){1}}}\multiput(0,0)(0,40){2}{\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\multiput(17,2)(0,32){2}{\sf{7 cm}}\put(9,17.5){\sf{h}}\end{picture}$

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$\star\;{\boxed{\sf{\pink{Volume_{\;(cylinder)}= \pi r^2h}}}}$

$:\implies\sf \dfrac{22}{ \cancel{7}} \times \cancel{7} \times 7 \times h = 2002$

$:\implies\sf 22 \times 7 \times h = 2002$

$:\implies\sf 154 \times h = 2002$

$:\implies\sf h = \cancel{ \dfrac{2002}{154}}$

$:\implies{\underline{\boxed{\frak{\purple{h = 13\:cm}}}}}\;\bigstar$

$\therefore\:{\underline{\sf{Height\;of\;cylinder\; {\textsf{\textbf{13\;cm}}}.}}}$

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Now, Finding Total surface area of cylinder,

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

$:\implies\sf TSA_{\;(cylinder)} = 2 \times \dfrac{22}{ \cancel{7}} \times \cancel{7} \bigg(13 + 7 \bigg)$

$:\implies\sf TSA_{\;(cylinder)} = 2 \times 22 \times 20$

$:\implies{\underline{\boxed{\frak{\purple{TSA_{\;(cylinder)}= 880\;cm^3 }}}}}\;\bigstar$

$\therefore\:{\underline{\sf{Total\:surface\:area\;of\;cylinder\; \bf{880\;cm^3}.}}}$