Question

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

10cm then its volume is​

Answer 1

Given :-

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

10cm

To Find :-

Volume

Solution :-

Let the radius be r

Perimeter = 2πr

44 = 2 × 22/7 × r

44 = 44/7 × r

44 × 7/44 = r

7 = r

Volume = πr²h

Volume = 22/7 × (7)² × 10

Volume = 22/7 × 49 × 10

Volume = 22 × 7 × 10

Volume = 220 × 7

Volume = 1540 cm³

Answer 2

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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