Question

find the height of cylinder whose radius is 7 cm and the total surface area is 968 cm square

Answer 1

total s. area of cylinder

Answer 2

Radius of cylinder is 7 cm.

Total surface area of Cylinder is 968 cm².

We have to find, height of cylinder.

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☯ Let height of cylinder be h cm.

We know that,

$\star\;{\boxed{\sf{\purple{TSA_{\;(cylinder)} = 2 \pi r(h + r)}}}}$

$\sf Here \begin{cases} & \sf{Radius, r = 7\;cm } \\ & \sf{TSA = 968\;cm^2} \end{cases}$

$\setlength{\unitlength}{1 cm} \thicklines \begin{picture}(2,0)\qbezier(0,0)(0,0)(0,2.5)\qbezier(2,0)(2,0)(2,2.5)\qbezier(0,0)(1,1)(2,0)\qbezier(0,0)( 1, - 1)(2,0) \put(2.3,1){\vector(0,1){1.5}}\put(2.3,1){\vector(0, - 1){1.2}}\put(2.3,1){ \bf h }\put(0.3,0.1){ \bf 7\:cm }\put(0,0){\vector(1,0){1}}\qbezier(0,2.5)(1,1.5)(2,2.5)\qbezier(0,2.5)(1, 3.5)(2,2.5)\end{picture}$

☯ Now, Putting values in formula,

$:\implies\sf 2 \times \dfrac{22}{7} \times 7(h + 7) = 968$

$:\implies\sf 44(h + 7) = 968$

$:\implies\sf h + 7 = \cancel{ \dfrac{968}{44}}$

$:\implies\sf h + 7 = 22$

$:\implies\sf h = 22 - 7$

$:\implies{\boxed{\frak{\pink{15\;cm}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Hence,\; Height\;of\;cylinder\;is\; \bf{15\;cm}.}}}$

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$\boxed{\underline{\underline{\bigstar \: \bf\:More\:\:know\:\bigstar}}}$

• Curved surface area, CSA of cylinder = $\sf 2 \pi rh$

• Volume of cylinder = $\sf \pi r^2 h$