Question

Find the total surface area of a hollow
cylindrical pipe of length 50 cm, external
diameter 12 cm and internal diameter 9 cm.-

Answer 1

Answer:

• 3399 cm²

GivEn :-

• Length of hollow cylindrical pipe is 50 cm
• External diameter is 12 cm
• internal dimeter is 9 cm

To Find :-

• The total surface area

Step-by-step explanation:

The external radius = 12 ÷ 2 = 6 cm

The internal radius = 9 ÷ 2 = 4.5 cm

CSA of the pipe,

$\implies \sf \: 2\pi h(R + r)$

• h = length
• R = External radius
• r = internal radius

$\implies \sf \: 2 \times \dfrac{22}{7} \times 50(6 + 4.5)$

$\implies \sf \: 2 \times \dfrac{22}{7} \times 50 \times 10.5$

$\implies \sf \: \dfrac{23100}{7}$

$\implies \boxed{ \red{ \bold{CSA = 3300 {cm}^{2} }}}$

Area of two circular sides,

$\implies \sf \: 2 \times \dfrac{22}{7} ( {6}^{2} - {4.5}^{2} )$

$\implies \sf \: 2 \times \dfrac{22}{7} \times 15.75$

$\implies \boxed{ \red{ \bold{99 {cm}^{2} }}}$

Now, the total surface area

$\implies \sf \: (3300 + 99) {cm}^{2}$

$\implies \boxed{ \red{ \bold{TSA = 3399 {cm}^{2} }}}$

Answer 2

${\bold{\sf{\underline{Understanding \: the \: question}}}}$

✪ This question says that we have to find the surface area of a hollow cylindrical pipe and it's length is given as 50 cm, it's external diameter is 12 cm and the internal diameter is 9 cm

${\bold{\sf{\underline{Given \: that}}}}$

✪︎ Length of hollow cylindrical pipe = 50 cm

✪︎ External diameter of hollow cylindrical pipe = 12 cm

✪ ︎Internal diameter of hollow cylindrical pipe = 9 cm

${\bold{\sf{\underline{To \: find}}}}$

✪ Total surface area of a hollow cylindrical pipe.

${\bold{\sf{\underline{Solution}}}}$

✪ Total surface area of a hollow cylindrical pipe = 3399 cm²

${\bold{\sf{\underline{Using \: concept}}}}$

✪ Formula to find total surface area of hollow cylinderal pipe ( according to the question ).

${\bold{\sf{\underline{Using \: formula}}}}$

✪ Total surface area of cylinder = 2πl ( E + ɪ ) ( according to the question )

${\bold{\sf{\underline{Where,}}}}$

✪ r denotes Radius

✪ l denotes length

✪ E denotes external diameter

✪ ɪ denotes internal diameter

✪ π pronounced as pi

✪ The value of π is 22/7

✪ Total surface area also written as T.S.A

✪ Curved surface area also written as C.S.A

${\bold{\sf{\underline{Convertation}}}}$

~ External diameter of hollow cylindrical pipe = 12 cm

➥ External radius of hollow cylindrical pipe = Diameter / 2

➥ External radius of hollow cylindrical pipe = 12 / 2

➥ External radius of hollow cylindrical pipe = 6 cm

~ Internal diameter of hollow cylindrical pipe = 9 cm

➥ Internal radius of hollow cylindrical pipe = Diameter / 2

➥ Internal radius of hollow cylindrical pipe = 9 / 2

➥ Internal radius of hollow cylindrical pipe = 4.5 cm

✪ Note : We convert diameter into radius because of a reason and the reason is that the formula to find total surface area of cylinder ( according to the question ) is 2πl ( E + ɪ ) and here as we know that r denotes Radius nor diameter thats why we change it !

${\bold{\sf{\underline{Full \: solution}}}}$

~ Finding curved surface area of a hollow cylindrical pipe

➨ 2πl ( E + ɪ )

➨ 2 × ${\sf{\dfrac{22}{7}}}$ × 50 ( 6 + 4.5 )

➨ 2 × ${\sf{\dfrac{22}{7}}}$ × 50 ( 10.5 )

➨ ${\sf{\dfrac{44}{7}}}$ × 50 ( 10.5 )

➨ ${\sf{\dfrac{44}{7}}}$ × 50 × 10.5

➨ ${\sf{\dfrac{44}{7}}}$ × 525

➨ 3300 cm²

• Henceforth, the C.SA. is 3300 cm²

~ Finding area of 2 circles

➨ 2 × ${\sf{\dfrac{22}{7}}}$ (6² - 4.5)²

➨ 2 × ${\sf{\dfrac{22}{7}}}$ ( 15.75 )

➨ 99 cm²

• Henceforth, 99 cm² is the area os 2 circles

~ Finding T.S.A

➨ 3300 + 99

➨ 3399 cm²

• Henceforth, 3399 cm² is the total surface area of hollow cylindrical pipe.

More knowledge -

Diagram of a cylinder -

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

Formula related to Cylinder -

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

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