Question

The curved surface area of a cylinder is 540 square centimetres .If its height is 300cm,then find the diameter of the base of the cylinder.(Take π=22/7)​

Answer 1

Given : The curved surface area of a cylinder of height 300 cm is 540 cm².

Need To Find : Base Diameter 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 540 cm² .

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

⠀⠀⠀⠀⠀$:\implies \sf { 2 \times \pi \times x \times 300 = 540 cm^{2} }$

⠀⠀⠀⠀⠀$:\implies \sf { \pi \times x \times 600 = 540 cm^{2} }$

⠀⠀⠀⠀⠀$:\implies \sf { \dfrac{22}{7} \times x \times 600 = 540 cm^{2} }$

⠀⠀⠀⠀⠀$:\implies \sf { x = \dfrac{540\times 7 }{22\times 600} }$

⠀⠀⠀⠀⠀$:\implies \sf { x = \dfrac{3780}{13200} }$

⠀⠀⠀⠀⠀$\underline {\boxed{\pink{ \mathrm {  x = 0.286\: cm}}}}\:\bf{\bigstar}$

Therefore,

⠀⠀⠀⠀⠀$\underline {\therefore\:{ \mathrm {  Base\:Radius \:of\:Cylinder \:is\:\bf{0.286\: cm}}}}$

⠀⠀⠀⠀⠀Finding Diameter using Radius of Cylinder :

⠀⠀⠀⠀⠀$\underline {\boxed {\sf{ Diameter = 2\times r \:units }}}$

⠀⠀⠀⠀⠀Here r is the Base Radius of Cylinder in cm .

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

⠀⠀⠀⠀⠀$:\implies \sf { Diameter = 2 \times 0.286 }$

⠀⠀⠀⠀⠀$\underline {\boxed{\pink{ \mathrm {  Diameter = 0.572\: cm}}}}\:\bf{\bigstar}$

Therefore,

⠀⠀⠀⠀⠀$\underline {\therefore\:{ \mathrm {  Hence,\:Base\:Diameter \:of\:Cylinder \:is\:\bf{0.572\: cm}}}}$

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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 540 cm² .

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

⠀⠀⠀⠀⠀$:\implies \sf { 2 \times \pi \times 0.286 \times 300 = 540 cm^{2} }$

⠀⠀⠀⠀⠀$:\implies \sf { 600 \times \pi \times 0.286 = 540 cm^{2} }$

⠀⠀⠀⠀⠀$:\implies \sf { 171.6 \times \pi = 540 cm^{2} }$

⠀⠀⠀⠀⠀$:\implies \sf { \cancel {171.6} \times \dfrac{22}{\cancel {7}} = 540 cm^{2} }$

⠀⠀⠀⠀⠀$:\implies \sf { 24.53 \times 22 = 540 cm^{2} }$

⠀⠀⠀⠀⠀$:\implies \sf { 539.66 cm^{2} = 540 cm^{2} }$

By doing Round off :

⠀⠀⠀⠀⠀$\underline {\boxed{\pink{ \mathrm {  540cm^{2} = 540\: cm^{2}}}}}\:\bf{\bigstar}$

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

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