Question

What is the volume of a cylinder , whose base diameter us of 20cm and height of 5cm.

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Answer 1

`\boxed{\tt \pink{Given:}}`

`\red\star`Diameter of base of a cylinder = 20 cm.

`\red\star`Height of cylinder = 5cm.

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`\boxed{\tt \pink{To~Find:}}`

`\red\star`Volume of Cylinder.

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`\boxed{\tt \pink{Solution}}`

To find volume of Cylinder first we should know radius of Cylinder. We can get radius by diameter using this formula:-

`\boxed{\rm Diameter = 2 radius}`

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`\hookrightarrow\sf Diameter = 2 radius`

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`\hookrightarrow\sf 20= 2 radius`

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`\hookrightarrow\sf (20)/(2)= radius`

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`\hookrightarrow\sf (2*10)/(2)= radius`

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`\hookrightarrow \sf (\cancel2*10)/(\cancel2)= radius`

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`\hookrightarrow \sf (1*10)/(1)= radius`

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`\hookrightarrow \sf 10= radius`

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`\hookrightarrow \bf radius = \pmb{\blue{10 cm}}`

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Now Finally Let's find volume of Cylinder.

we know:-

`\boxed{\rm Volume ~ of ~ Cylinder = \pi radius^2 * height}`

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So:-

`\dashrightarrow\sf Volume ~of ~Cylinder = \pi radius^2* height\\`

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`\dashrightarrow\sf Volume ~of ~Cylinder = \pi (10)^2* 5\\`

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`\dashrightarrow\sf Volume ~of ~Cylinder = \pi 10*10*5\\`

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`\dashrightarrow\sf Volume ~of ~Cylinder = \pi 100*5\\`

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`\dashrightarrow\sf Volume ~of ~Cylinder = \pi* 500\\`

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`\dashrightarrow\sf Volume ~of ~Cylinder = (22)/(7)* 500\\`

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`\dashrightarrow\sf Volume ~of ~Cylinder = (11000)/(7)\\`

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`\dashrightarrow\bf Volume ~of ~Cylinder =\pmb{\blue{1,571.4~cm}}\\`

KNOW MORE:-

`\begin{gathered}\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc}\small\underline{\sf{\pmb{ \gray{More \: Formulae}}}} \\ \\ \bigstar \: \bold{CSA_((cylinder)) = 2\pi \: rh}\\ \\\bigstar \: \bold{Volume_((cylinder)) = \pi {r}^(2) h}\\ \\ \bigstar \: \bold{TSA_((cylinder)) = 2\pi \: r(r + h)}\\ \\ \bigstar \: \bold{CSA_((cone)) = \pi \: r \: l}\\ \\ \bigstar\: \bold{TSA_((cone)) = \pi \: r \: (l + r)}\\ \\ \bigstar \: \bold{Volume_((sphere)) = (4)/(3)\pi {r}^(3) }\\ \\ \bigstar \: \bold{Volume_((cube)) ={(side)}^(3) }\\ \\ \bigstar \: \bold{CSA_((cube)) = 4 {(side)}^(2) }\\ \\ \bigstar \: \bold{TSA_((cube)) = 6 {(side)}^(2) }\\ \\\bigstar \: \bold{Volume_((cuboid)) = lbh}\\ \\ \bigstar \: \bold{CSA_((cuboid)) = 2(l + b)h}\\ \\ \bigstar \: \bold{TSA_((cuboid)) = 2(lb +bh+hl )}\\ \: \end{array} }}\end{gathered}\end{gathered}\end{gathered}\end{gathered}`