Question

The perimeter of the base of a right circular cylinder is 44 cm. And the height of the cylinder is 10 cm. then it's curved surface area is​

Answer 1

Given information,

The perimeter of the base of a right circular cylinder is 44 cm. And the height of the cylinder is 10 cm. Then it's curved surface area is?

• Perimeter of base of cylinder = 44 cm
• Height of cylinder = 10 cm
• C.S.A of cylinder = ?

As we know that base of right circular cylinder is circular in shape.

Using formula,

✪ Perimeter of circle = 2πr ✪

Where,

• π = Pi
• r = radius of base of cylinder

We have,

• π = 22/7
• Perimeter of base = 44 cm

Putting all values,

➻ 88 = 2 × 22/7 × r

➻ 88 = 44/7 × r

➻ r = 88 × 7/44

➻ r = 2 × 7

➻ r = 14

• Henceforth, radius of ase of right circular cylinder is 14 cm.

Now,

• We know that •

✪ C.S.A of cylinder = 2πrh ✪

Where,

• π = Pi
• r = radius of base of cylinder
• h = height of cylinder

We have,

• π = 22/7
• r = 14 cm
• h = 10 cm

Putting all values,

➻ C.S.A of cylinder = 2 × 22/7 × 14 × 10

➻ C.S.A of cylinder = 2 × 22 × 2 × 10

➻ C.S.A of cylinder = 44 × 2 × 10

➻ C.S.A of cylinder = 88 × 10

➻ C.S.A of cylinder = 880 cm²

• Henceforth, curved surface area of right circular cylinder is 880 cm².

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Answer 2

Answer:

$\begin{gathered}{\underline{\underline{\maltese{\textsf{\textbf{\:Given :}}}}}}\end{gathered}$

• ➜ The perimeter of the base of a right circular cylinder = 44 cm
• ➜ Height of the cylinder = 10 cm

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

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

• ➜ Curved surface area of cylinder

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

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

$\bigstar{\underline{\boxed{\bf{\red{Perimeter \: of \: cylinder = 2 \pi r}}}}}$

$\bigstar{\underline{\boxed{\bf{\red{Curved \: surface \: area \: of \: cylinder =2 \pi rh}}}}}$

$\green\bigstar$ Where

• ➬ π = 22/7
• ➬ r = radius
• ➬ h = height

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

$\begin{gathered}{\underline{\underline{\maltese{\textsf{\textbf{\:Solution :}}}}}}\end{gathered}$

$\green\bigstar$ Here

• ➬ Perimeter of Cylinder = 44 cm
• ➬ Height of the cylinder = 10 cm

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

$\green\bigstar$ Firstly, Finding the radius of cylinder

${\dashrightarrow{\pmb{\sf{Perimeter \: of \: cylinder = 2 \pi r}}}}$

• Substuting the values

${\dashrightarrow{\sf{88 \: cm= 2 \times \dfrac{22}{7} \times r}}}$

${\dashrightarrow{\sf{88 \: cm= \dfrac{2 \times 22}{7} \times r}}}$

${\dashrightarrow{\sf{88 \: cm= \dfrac{44}{7} \times r}}}$

${\dashrightarrow{\sf{Radius_{(Cylinder)} = 88 \times \dfrac{7}{44} }}}$

${\dashrightarrow{\sf{Radius_{(Cylinder)} = \cancel{88} \times \dfrac{7}{\cancel{44}}}}}$

${\dashrightarrow{\sf{Radius_{(Cylinder)} =2 \times 7 }}}$

${\dashrightarrow{\sf{Radius_{(Cylinder)} =14 \: cm }}}$

$\bigstar{\underline{\boxed{\bf{\purple{Radius \: of \: cylinder=14 \: cm }}}}}$

∴ The radius of cylinder is 14 cm.

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

$\green\bigstar$ Now, Finding the curved surface area of cylinder

${\dashrightarrow{\pmb{\sf{Curved \: surface \: area \: of \: cylinder =2 \pi rh}}}}$

• Substuting the values

${\dashrightarrow{\sf{Curved \: surface \: area \: of \: cylinder =2 \times \dfrac{22}{7} \times 10 \times 14}}}$

${\dashrightarrow{\sf{Curved \: surface \: area \: of \: cylinder = \dfrac{2 \times 22 \times 10 \times 14}{7}}}}$

${\dashrightarrow{\sf{Curved \: surface \: area \: of \: cylinder = \dfrac{6160}{7}}}}$

${\dashrightarrow{\sf{Curved \: surface \: area \: of \: cylinder = \cancel{\dfrac{6160}{7}}}}}$

${\dashrightarrow{\sf{Curved \: surface \: area \: of \: cylinder = 880 \: {cm}^{2} }}}$

${\bigstar\underline{\boxed{\bf{\purple{Curved \: surface \: area \: of \: cylinder = 880 \: {cm}^{2}}}}}}$

∴ The curved surface area of cylinder is 880 cm².

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

$\begin{gathered}{\underline{\underline{\maltese{\textsf{\textbf{\:Additional Information :}}}}}}\end{gathered}$

$\quad$↠ 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

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

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

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

https://brainly.in/question/8927859

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