Question

The radius of a cylinder is 7cm and is height is 10cm. Find the curved surface

and total surface area.​

Answer 1

Answer:

curved surface area=440 cm. square

total surface area = 748 cm.square

Answer 2

Answer:

${\large{\underline{\underline{\pmb{\frak{Given:-}}}}}}$

• ★ Radius of Cylinder = 7 cm
• ★ Height of Cylinder = 10 cm

$\begin{gathered}\end{gathered}$

${\large{\underline{\underline{\pmb{\frak{To \: Find:-}}}}}}$

• ★ Curved surface area of Cylinder
• ★ Total surface area of Cylinder

$\begin{gathered}\end{gathered}$

${\large{\underline{\underline{\pmb{\frak{Using \: Formulae:-}}}}}}$

$\quad\bigstar{\underline{\boxed{ \sf{C.S.A \: of \: Cylinder =2 \pi rh }}}}$

$\quad\bigstar{\underline{\boxed{ \sf{ T.S.A\: of \: Cylinder =2 \pi r(r + h)}}}}$

Where

• ★ C.S.A = Curved surface area
• ★ T.S.A = Total surface area
• ★ r = radius
• ★ h = height
• ★ π = 22/7

$\begin{gathered}\end{gathered}$

${\large{\underline{\underline{\pmb{\frak{Diagram:-}}}}}}$

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

$\begin{gathered}\end{gathered}$

${\large{\underline{\underline{\pmb{\frak{Solution:-}}}}}}$

$\red\bigstar$ Finding Total curved surface area of Cylinder,

$\quad\dashrightarrow{ \sf{C.S.A \: of \: Cylinder =2 \pi rh }}$

• Substuting the values

${\quad\dashrightarrow{ \sf{C.S.A \: of \: Cylinder =2 \times \dfrac{22}{7} \times 7 \times 10}}}$

${\quad\dashrightarrow{ \sf{C.S.A \: of \: Cylinder = \dfrac{2 \times 22 \times 7 \times 10}{7}}}}$

${\quad\dashrightarrow{ \sf{C.S.A \: of \: Cylinder = \dfrac{3080}{7}}}}$

${\quad\dashrightarrow{ \sf{C.S.A \: of \: Cylinder = \cancel\dfrac{3080}{7}}}}$

${\quad\dashrightarrow{ \sf{C.S.A \: of \: Cylinder = 440 \: {cm}^{2}}}}$

${\quad{\bigstar{\underline{\boxed{ \sf{C.S.A \: of \: Cylinder = 440 \: {cm}^{2}}}}}}}$

∴ Curved surface area of Cylinder is 440 cm².

$\begin{gathered}\end{gathered}$

$\red\bigstar$ Finding the total surface area of Cylinder,

${\quad{\dashrightarrow{ \sf{ T.S.A\: of \: Cylinder =2 \pi r(r + h)}}}}$

${\quad{\dashrightarrow{ \sf{ T.S.A\: of \: Cylinder =2 \times \dfrac{22}{7} \times 7(7 + 10)}}}}$

${\quad{\dashrightarrow{ \sf{ T.S.A\: of \: Cylinder =\dfrac{2 \times 22 \times 7}{7} \times (17)}}}}$

${\quad{\dashrightarrow{ \sf{ T.S.A\: of \: Cylinder =\dfrac{308 \times 17}{7}}}}}$

${\quad{\dashrightarrow{ \sf{ T.S.A\: of \: Cylinder =\dfrac{5236}{7}}}}}$

${\quad{\dashrightarrow{ \sf{ T.S.A\: of \: Cylinder = \cancel\dfrac{5236}{7}}}}}$

${\quad{\dashrightarrow{ \sf{ T.S.A\: of \: Cylinder =748 \: {cm}^{2} }}}}$

${\quad{\bigstar{\underline{\boxed{\sf{ T.S.A\: of \: Cylinder =748 \: {cm}^{2} }}}}}}$

∴ Total surface area of Cylinder is 748 cm².

$\begin{gathered}\end{gathered}$

${\large{\underline{\underline{\pmb{\frak{Learn \: More : -}}}}}}$

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

$\begin{gathered}\end{gathered}$

${\large{\underline{\underline{\pmb{\frak{Request:-}}}}}}$

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