Question

a right circular cylinder has height of 8cm and radius of 7cm. find its a) curved surface b)total surface area​

Answer 1

Given : A right circular cylinder has height of 8cm and radius of 7cm.

Need To Find : Curved Surface area and Total Surface Area .

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❍ Finding Total Surface Area of Cylinder :

⠀⠀⠀⠀⠀Formula for Total Surface Area is Given by :

$\underline {\frak{\dag As, \:We\:know\:that,\:}}$

$\qquad \quad \underline {\boxed {\sf{\star Total \:Surface \:Area\:_{(Cylinder)} = 2 \pi r (r + h) \:sq.units}}}$

Where ,

• r is the Radius of Cylinder h is the Height of Cylinder & $\pi = \dfrac{22}{7}$.

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

$:\implies \sf{ Total \:Surface \:Area = 2 \times \pi \times 7 ( 7 + 8) }\\\\:\implies \sf{ Total \:Surface \:Area = 2 \times \pi \times 7 \times 15 }\\\\ :\implies \sf{ Total \:Surface \:Area = 2 \times \dfrac{22}{\cancel{7}} \times \cancel {7}\times 15 }\\\\ :\implies \sf{ Total \:Surface \:Area = 2 \times 22 \times 15 }\\\\:\implies \sf{ Total \:Surface \:Area = 44 \times 15 }\\\\\underline {\boxed{\pink{ \mathrm {  Total \:Surface\:Area\:= 660\: cm^{2}}}}}\:\bf{\bigstar}$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {Hence, \: Total \:Surface \:Area\:of\:Cylinder \:is\:\bf{660\: cm^{2}}}}}$

❍ Finding Curved Surface Area of Cylinder :

⠀⠀⠀⠀⠀Formula for Curved Surface Area is Given by :

$\underline {\frak{\dag As, \:We\:know\:that,\:}}$

$\qquad \quad \underline {\boxed {\sf{\star Total \:Surface \:Area\:_{(Cylinder)} = 2 \pi rh \:sq.units}}}$

Where ,

• r is the Radius of Cylinder h is the Height of Cylinder & $\pi = \dfrac{22}{7}$.

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

$:\implies \sf{ Curved \:Surface \:Area = 2 \times \dfrac{22}{7} \times 7 \times 8 }\\\\:\implies \sf{ Curved \:Surface \:Area = 2 \times \dfrac{22}{\cancel{7}} \times \cancel {7}\times 8 }\\\\ :\implies \sf{ Curved \:Surface \:Area = 2 \times 22 \times 8 }\\\\:\implies \sf{ Curved \:Surface \:Area = 44 \times 8 }\\\\\underline {\boxed{\pink{ \mathrm { Curved \:Surface\:Area\:= 352\: cm^{2}}}}}\:\bf{\bigstar}$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {Hence,  \:Curved \:Surface \:Area\:of\:Cylinder \:is\:\bf{352\: cm^{2}}}}}$

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