Question

The curved surface area of a cylinder of height 8 cm is 176 cm². Find the radius of the base.​

Answer 1

Given : The curved surface area of a cylinder of height 8 cm is 176 cm².

Need To Find : Base Radius of of Cylinder.

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❍ Let's consider Base Radius of Cylinder be x .

$\underline {\frak{ As, \:We\:Know\:that\:}}$

⠀⠀⠀⠀⠀$\underline {\boxed {\sf{ Curved \:Surface \:Area\:_{(Cylinder)} = 2\pi r h \:sq.units }}}$

⠀⠀⠀⠀⠀Here r is the Base Radius of Cylinder in cm , h is the Height of Cylinder in cm and $\pi=\:\dfrac{22}{7}$ and we have given with Curved surface area of Cylinder is 176 cm² .

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

⠀⠀⠀⠀⠀$:\implies \sf { 2 \times \pi \times x \times 8 = 176 cm^{2} }$

⠀⠀⠀⠀⠀$:\implies \sf { \pi \times x \times 16 = 176 cm^{2} }$

⠀⠀⠀⠀⠀$:\implies \sf { \dfrac{22}{7} \times x \times 16 = 176 cm^{2} }$

⠀⠀⠀⠀⠀$:\implies \sf { x = \dfrac{176\times 7 }{22\times 16} }$

⠀⠀⠀⠀⠀$:\implies \sf { x = \dfrac{1232}{352} }$

⠀⠀⠀⠀⠀$\underline {\boxed{\pink{ \mathrm {  x = 3.5\: cm}}}}\:\bf{\bigstar}$

Therefore,

⠀⠀⠀⠀⠀$\underline {\therefore\:{ \mathrm {  Base\:Radius \:of\:Cylinder \:is\:\bf{3.5\: cm}}}}$

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$\large {\boxed {\sf{ \mid {\overline {\underline { \bigstar Verification \:}}}\mid}}}$

$\underline {\frak{ As, \:We\:Know\:that\:}}$

⠀⠀⠀⠀⠀$\underline {\boxed {\sf{ Curved \:Surface \:Area\:_{(Cylinder)} = 2\pi r h \:sq.units }}}$

⠀⠀⠀⠀⠀Here r is the Base Radius of Cylinder in cm , h is the Height of Cylinder in cm and $\pi=\:\dfrac{22}{7}$ and we have given with Curved surface area of Cylinder is 176 cm² .

⠀⠀⠀⠀⠀⠀$\underline {\bf{\star\:Now \: By \: Substituting \: the \: Found \: Values \::}}$

⠀⠀⠀⠀⠀$:\implies \sf { 2 \times \pi \times 3.5 \times 8 = 176 cm^{2} }$

⠀⠀⠀⠀⠀$:\implies \sf { 16 \times \pi \times 3.5 = 176 cm^{2} }$

⠀⠀⠀⠀⠀$:\implies \sf { 56 \times \pi = 176 cm^{2} }$

⠀⠀⠀⠀⠀$:\implies \sf { \cancel {56} \times \dfrac{22}{\cancel {7}} = 176 cm^{2} }$

⠀⠀⠀⠀⠀$:\implies \sf { 8 \times 22 = 176 cm^{2} }$

⠀⠀⠀⠀⠀$\underline {\boxed{\pink{ \mathrm {  176cm^{2} = 176\: cm^{2}}}}}\:\bf{\bigstar}$

⠀⠀⠀⠀⠀$\therefore \bf{ Hence \:Verified \:}$

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