Question

find the curved surface area of the cylinder whose circumference is 44cm and height 10cm ​

Answer 1

✠ SolutioN :-

• Circumference of the base of cylinder = 44cm.
• Height of the cylinder = 10cm.

As we know that,

★ Circumference of cylinder = 2πr

⇒ 2πr = 44.

⇒ 2 x 22/7 x r = 44.

⇒ 44/7 x r = 44.

⇒ r = 7cm.

★ Curved surface area of cylinder = 2πrh

⇒ 2 x 22/7 x 7 x 10.

⇒ 2 x 22 x 10

⇒ 440cm²

Answer 2

Answer:

$\underline{\underline{\bigstar{\textbf{\textsf{\: GivEn\::-}}}}}$

• ↠ Circumference of cylinder = 44 cm
• ↠ Height of cylinder = 10 cm

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

$\underline{\underline{\bigstar{\textbf{\textsf{\:To FinD\::-}}}}}$

• ↠ Curved surface area of cylinder

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

$\underline{\underline{\bigstar{\textbf{\textsf{\:UsinG FormuLa\::-}}}}}$

$\quad\dag{\underline{\boxed{\sf{Circumference \: of \: cylinder = 2 \pi r}}}}$

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

Where

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

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

$\underline{\underline{\bigstar{\textbf{\textsf{\:ConcepT\::-}}}}}$

↠ Here the concept of curved surface area of cylinder has been used. We are given circumference of cylinder is 44 cm and height of cylinder is 10 cm. We need to find the curved surface area of Cylinder. So, firstly we will find the radius of cylinder and then after finding radius of cylinder we will find the curved surface area of Cylinder by using formula..

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

$\underline{\underline{\bigstar{\textbf{\textsf{\:DiaGram\::-}}}}}$

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

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

$\underline{\underline{\bigstar{\textbf{\textsf{\:SoluTion\::-}}}}}$

$\red\bigstar$ Here :-

• Circumference = 44 cm
• Height = 10 cm

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

$\red\bigstar$ Firstly, Calculating the radius of cylinder

$\quad{\dashrightarrow{\sf{Circumference \: of \: cylinder = 2 \pi r}}}$

• Substuting the values

$\quad{\dashrightarrow{\sf{ 44= 2 \times \dfrac{22}{7} \times r}}}$

$\quad{\dashrightarrow{\sf{ 44= \dfrac{2 \times 22}{7} \times r}}}$

$\quad{\dashrightarrow{\sf{ 44= \dfrac{44}{7} \times r}}}$

$\quad{\dashrightarrow{\sf{ 44 \times \dfrac{7}{44} = r}}}$

$\quad{\dashrightarrow{\sf{ \cancel{44}\times \dfrac{7}{\cancel{44}}= r}}}$

$\quad{\dashrightarrow{\sf{{7} = r}}}$

$\quad\bigstar{\underline{\boxed{\pmb{\sf{\purple{Radius \: of \: Cylinder = 7 cm}}}}}}$

∴ The Radius of Cylinder is 7 cm.

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

$\red\bigstar$ Now, Finding the curved surface area of cylinder :-

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

• Substuting the values

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

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

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

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

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

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

∴ The curved surface area of cylinder is 440 cm².

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

$\underline{\underline{\bigstar{\textbf{\textsf{\:LearN MorE\::-}}}}}$

$\quad$ ↠ Volume of cylinder = πr²h

$\quad$ ↠ T.S.A of cylinder = 2πrh + 2πr²

$\quad$ ↠ Volume of cone = ⅓ πr²h

$\quad$ ↠ C.S.A of cone = πrl

$\quad$ ↠ T.S.A of cone = πrl + πr²

$\quad$ ↠ Volume of cuboid = l × b × h

$\quad$ ↠ C.S.A of cuboid = 2(l + b)h

$\quad$ ↠ T.S.A of cuboid = 2(lb + bh + lh)

$\quad$ ↠ C.S.A of cube = 4a²

$\quad$ ↠ T.S.A of cube = 6a²

$\quad$ ↠ Volume of cube = a³

$\quad$ ↠ Volume of sphere = 4/3πr³

$\quad$ ↠ Surface area of sphere = 4πr²

$\quad$ ↠ Volume of hemisphere = ⅔ πr³

$\quad$ ↠ C.S.A of hemisphere = 2πr²

$\quad$ ↠ T.S.A of hemisphere = 3πr²

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

$\underline{\underline{\bigstar{\textbf{\textsf{\:RequesT\::-}}}}}$

• ★ If there is any difficulty viewing this answer in app, kindly see this answer at website Brainly.in for clear steps and understanding.
• ★ Here is the question link : https://brainly.in/question/8927859

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬