Question

If the curved surface area of a right circular cylinder whose base radius and height are equal is 72piecm^2, then the diameter of the base is​

Answer 1

Given : The curved surface area of a right circular cylinder whose base radius and height are equal is 72$\pi$ cm² .

Exigency To Find : The Diameter of Base .

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❍ Let's Consider r be the Radius of Cylinder.

⠀⠀⠀⠀⠀Formula for Curved Surface area of Cylinder is given by :

$\dag\:\:\boxed {\sf { Curved \:Surface \:Area_{(Cylinder)} = \bigg( 2\pi r h\bigg)}}$

Where ,

• r is the Radius of Circle and h is the Height of Cylinder .

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

$\qquad:\implies \sf { 72 \pi = 2 \times \pi \times r \times h }$

Given that ,

• The base radius and height of Cylinder are equal .

$\qquad:\implies \sf { 72 \pi = 2 \pi \times r \times r }$

$\qquad:\implies \sf { 72 \pi = 2 \pi \times r^2 }$

$\qquad:\implies \sf { \cancel {\dfrac{72 \pi}{2\pi}} = r^2}$

$\qquad:\implies \sf { 36 = r^2 }$

$\qquad:\implies \sf { \sqrt {36} = r }$

$\qquad:\implies \bf { r = 6 cm }$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {  Radius \:of\:Cylinder \:is\:\bf{6\: cm}}}}$

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As , We know that ,

• $\dag\:\:\boxed {\sf { Base\:Diameter_{(Cylinder)} = \bigg( 2\times Radius \bigg)}}$

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

$\qquad:\implies \sf { Diameter = 6 \times 2 }$

$\qquad:\implies \bf { Diameter = 12cm }$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {  Diameter \:of\:Cylinder \:is\:\bf{12\: cm}}}}$

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Answer 2

Step-by-step explanation:

Answer to ur question is 12 cm.