Math, asked by Anonymous, 10 months ago

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A cylinder has its height equal to its diameter find the ratio between its curved surface and the total surface.

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Answers

Answered by Anonymous
6

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Let, the height be 'h' units, then radius is'h/2'units

TSA of cylinder =2pir(h+r)

=2xpixh/2(h+h/2)

=2xpixh/2x3h/2

=3pih^2/2

CSA of cylinder =2pirh

=2pih/2h

= PIh^2

Ratio of CSA AND TSA

=pih^2:3pih^2/2

=1:3/2

=2:3

Ratio=2:3.....

Answered by CharmingPrince
10

\huge{\bigstar}{ \green{ \mathfrak{ \underline{ \underline{Question}}}}}{\bigstar}

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A cylinder has its height equal to its diameter find the ratio between its curved surface and the total surface</font>

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\huge{\bigstar}{ \green{ \mathfrak{ \underline{ \underline{Answer}}}}}{\bigstar}

\boxed{\red{\bold{Measurements:}}}

Radius = r

Diameter = 2r

Height = diameter = 2r

\boxed{\red{\bold{Curved \ surface \ area:}}}

\red{\implies}2 \pi rh

\red{\implies}2 \pi r(2r)

\red{\implies}2 \pi × 2r^2

\red{\implies}4 \pi r^2

\boxed{\red{\bold{Total \ surface \ area:}}}

\blue{\implies}2 \pi r(r+h)

\blue{\implies}2 \pi r (r+2r)

\blue{\implies}2 \pi r × 3r

\blue{\implies}6 \pi r^2

\boxed{\red{\bold{Ratio:}}}

\purple{\implies \displaystyle{\frac{Curved \ surface \ area}{Total \ surface \ area}} = \frac{4 \pi r^2}{6 \pi r^2}}

\green{\implies}\displaystyle{\frac{Curved \ surface \ area}{Total \ surface \ area}} = \frac{2}{3}

\green{\boxed{\implies{\boxed{2:3}}}}

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