Math, asked by pooja680, 3 months ago

The perimeter of the base of a right circular cylinder is 44cm and its height is 10cm then its volume is​

Answers

Answered by hotcupid16
156

Answer:-

\begin{gathered}{\large{\textsf{\textbf{\underline{\underline{Given :}}}}}}\end{gathered}

➳ The perimeter of the base of a right circular cylinder is 44cm and its height is 10cm

\begin{gathered}\end{gathered}

\begin{gathered}{\large{\textsf{\textbf{\underline{\underline{To Find :}}}}}}\end{gathered}

Volume of Cylinder

\begin{gathered}\end{gathered}

\begin{gathered}{\large{\textsf{\textbf{\underline{\underline{Using Formulae :}}}}}}\end{gathered}

 \dag{\underline{\boxed{\sf{Perimeter \:  of  \: Cylinder =  2{\pi}r}}}}

 \dag{\underline{\boxed{\sf{Volume \:  of  \: Cylinder =  {\pi}{r}^{2}h}}}}

Where

  • ➽ π = 22/7
  • ➽ r = radius
  • ➽ = height

\begin{gathered}\end{gathered}

\begin{gathered}{\large{\textsf{\textbf{\underline{\underline{Solution :}}}}}}\end{gathered}

{\dag{\underline{\underline{\pmb{\frak{\red{Here, }}}}}}}

  • ➽ π = 22/7
  • ➽ Height of Cylinder = 10 cm
  • ➽ Perimeter of Cylinder = 44 cm

\begin{gathered}\end{gathered}

{\dag{\underline{\underline{\pmb{\frak{\red{Firstly, Finding \:  the  \: radius \:  of  \: cylinder}}}}}}}

{: \implies{\sf{Perimeter \:  of  \: Cylinder =  2{\pi}r}}}

Substuting the values

{: \implies{\sf{44 \: cm =  2 \times {\dfrac{22}{7}} \times r}}}

{: \implies{\sf{44 \: cm = {\dfrac{2 \times 22}{7}} \times r}}}

{: \implies{\sf{44 \: cm = {\dfrac{44}{7}} \times r}}}

{: \implies{\sf{44 \: \times  \dfrac{7}{44} = r}}}

{: \implies{\sf{ \cancel{44} \: \times {\dfrac{7}{\cancel{44}}} = r}}}

{: \implies{\sf{7 = r}}}

\bigstar{\underline{\boxed{\sf{\blue{Radius \:  of  \: Cylinder} =  \purple{7  \: cm}}}}}

The Radius of Cylinder is 7 cm.

\begin{gathered}\end{gathered}

{\dag{\underline{\underline{\pmb{\frak{\red{Now,Finding \:  the \:  volume  \: of \:  cylinder}}}}}}}

: \implies{\sf{Volume \:  of  \: Cylinder =  {\pi}{r}^{2}h}}

Substuting the values

{: \implies{\sf{Volume \:  of  \: Cylinder =  {\dfrac{22}{7}} \times {(7)}^{2} \times 10}}}

{: \implies{\sf{Volume \:  of  \: Cylinder =  {\dfrac{22}{7}} \times {7 \times 7} \times 10}}}

{: \implies{\sf{Volume \:  of  \: Cylinder =  {\dfrac{22 \times 7 \times 7 \times 10}{7}}}}}

{: \implies{\sf{Volume \:  of  \: Cylinder =  {\dfrac{10780}{7}}}}}

{: \implies{\sf{Volume \:  of  \: Cylinder =  {\cancel{\dfrac{10780}{7}}}}}}

{: \implies{\sf{Volume \:  of  \: Cylinder = 1540 \:  {cm}^{3}}}}

\bigstar{\underline{\boxed{\sf{\blue{Volume \:  of  \: Cylinder} =  \purple{1540 \:  {cm}^{3}}}}}}

∴ The volume of cylinder is 1540 cm³

\begin{gathered}\end{gathered}

\begin{gathered}{\large{\textsf{\textbf{\underline{\underline{Diagram :}}}}}}\end{gathered}

\setlength{\unitlength}{1mm}\begin{picture}(5,5)\thicklines\multiput(-0.5,-1)(26,0){2}{\line(0,1){40}}\multiput(12.5,-1)(0,3.2){13}{\line(0,1){1.6}}\multiput(12.5,-1)(0,40){2}{\multiput(0,0)(2,0){7}{\line(1,0){1}}}\multiput(0,0)(0,40){2}{\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\multiput(18,2)(0,32){2}{\sf{7}}\put(9,17.5){\sf{10}}\end{picture}

➽ See the diagram from website Brainly.in.

➽ Here is the question link :

https://brainly.in/question/43396537

\begin{gathered}\end{gathered}

\begin{gathered}{\large{\textsf{\textbf{\underline{\underline{Learn More :}}}}}}\end{gathered}

\boxed{\begin{minipage}{6.2 cm}\bigstar$\:\underline{\textbf{Formulae Related to Cylinder :}}\\\\\sf {\textcircled{\footnotesize\textsf{1}}} \:Area\:of\:Base\:and\:top =\pi r^2 \\\\ \sf {\textcircled{\footnotesize\textsf{2}}} \:\:Curved \: Surface \: Area =2 \pi rh\\\\\sf{\textcircled{\footnotesize\textsf{3}}} \:\:Total \: Surface \: Area = 2 \pi r(h + r)\\ \\{\textcircled{\footnotesize\textsf{4}}} \: \:Volume=\pi r^2h\end{minipage}}

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Attachments:
Answered by CᴀᴘᴛᴀìɴLᴇᴠí
0

Answer:

  • 1540cm^3

Step-by-step explanation:

Given:

  • Circumference of cyclinde = 44cm
  • Height of cyinder = 10cm

To find:

  • Volume of cylinder

To find volume of cylinder we need radius

➠ Circumference of cylinder = 2πr

➠ 44 = 2×22/7 × r

➠ 44 = 44/7 × r

By Doing cross multiplication

➠ 44×7/44 × 1= r

➠ r = 7cm

Now let's find Volume:

➠ Volume of cylinder = πr² × h

➠ Volume = 22/7 × 7 × 7 × 10

➠ Volume = 22/7 × 49 × 10

➠ Volume = 22 × 7 × 10

➠ Volume = 1540cm^3

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