Question

find the height of cylinder whole radius is 7 centimetre and the total surface area is 968cm ​

Answer 1

Given : The Radius of Cylinder is 7 cm and the total surface area is 968cm² .

Need To Find : Height of Cylinder.

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❒ Let's consider the Height of Cylinder be x cm .

$\dag\:\cal{As,\:We\:know\:that\::}$

$\qquad \quad \dag\:\:\bigg\lgroup \sf { Total \:Surface\:Area_{(Cylinder)} = 2\pi r( r + h) }\bigg\rgroup$

⠀⠀⠀⠀Here r is the Radius of Cylinder and h is the Height of Cylinder and $\pi =\dfrac{22}{7}$

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: Given \: Values \::}}$

$\qquad \longmapsto \sf{968 = 2 \times \dfrac{22}{7} \times 7 (7 + x) }$

$\qquad \longmapsto \sf{968 = 2 \times \dfrac{22}{\cancel {7}} \times \cancel {7} (7 + x ) }$

$\qquad \longmapsto \sf{968 = 2 \times 22 (7 + x ) }$

$\qquad \longmapsto \sf{968 = 44 (7 + x ) }$

$\qquad \longmapsto \sf{\cancel {\dfrac {968}{44}} = 7 + x }$

$\qquad \longmapsto \sf{22 = 7 + x }$

$\qquad \longmapsto \sf{22 - 7 = x }$

$\qquad \longmapsto \boldsymbol{\purple {\underline { x = 15\:cm }}}$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {  Height \:of\:Cylinder \:is\:\bf{15\: cm}}}}$

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