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a metal pipe is 77cm long the inner diameter of a cross section is 4 cm the outer diameter being 4.4 cm .
Find its :
(i.) Inner curved Surface area
(ii.)Outer curved Surface area
(iii.)Total Surface area.



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Answer 1

Answer:

The inner radius, outer radius, and height of the cylinder are r, R, and h respectively.

Inner curved surface area = 2πrh

Outer curved surface area = 2πRh

Length of the pipe, h = 77 cm

Inner radius(r) of the pipe and outer radius(R) of the pipe are:

r = 4/2 cm = 2 cm

R = 4.4/2 cm = 2.2 cm

i) Inner curved surface area = 2πrh

= 2 × 22/7 × 2 cm × 77 cm

= 968 cm²

ii) Outer curved surface area = 2πRh

= 2 × 22/7 × 2.2 cm × 77 cm

= 1064.8 cm²

iii) The total surface area of the pipe can be obtained by adding the inner and outer curved surface areas along with the area of both the circular ends.

We can find the area of circular ends by subtracting the area of the inner circle from the outer circle area.

Area of both the circular ends of the pipe = 2 π (R² - r²)

TSA of pipe = CSA of inner surface + CSA of outer surface + Area of both the circular ends of the pipe

Hence, TSA of the pipe = 2πrh + 2πRh + 2π(R² - r²)

Now, area of both the circular ends of the pipe = 2π(R² - r²)

= 2 × 22/7 × [(2.2 cm)² - (2 cm)²]

= 2 × 22/7 × [4.84 cm² - 4 cm²]

= 2 × 22/7 × 0.84 cm²

= 5.28 cm²

Total surface area = 2πrh + 2πRh + 2π (R² - r²)

= 968 cm² + 1064.8 cm² + 5.28 cm² [Since, Inner curved surface area = 968 cm², Outer curved surface area = 1064.8 cm²]

= 2038.08 cm²

Mark it as the brainliest answer.

Answer 2

Step-by-step explanation:

$\huge\mathcal{\fcolorbox{aqua}{azure}{\red{✿Answer❖}}}$

Given:-

• a metal pipe is 77cm long.
• the inner diameter of a cross section is 4 cm.
• the outer diameter being 4.4 cm.

To find:-

• (i) Inner curved Surface area
• (ii)Outer curved Surface area
• (iii)Total Surface area.

Solution:-

$Inner \: radius \: (r _{1}) \: of \: cylindrical \: pipe =$

$= \: \: \frac{4}{2} \: cm$

$= \: 2 \: cm$

$Outer \: radis \: (r _{2}) \: of \: cylindrical \: pipe =$

$= \: \frac{4.4}{2} \: cm$

$= \: 2.2 \: cm$

$Height \:(h) \: of \: cylindrical \: pipe \: = \\ length \: of \: cylindrical \: pipe \: = \: 77cm$

$(i) \: CSA \: of \: inner \: surface \: of \: pipe =$

$= 2\pi \: r _{1} h$

$= \: (2 \: \times \: \frac{22}{7} \: \times \: 2 \: \times \: 77)cm {}^{2}$

$= \: 968 \: cm {}^{2}$

$(ii) \: CSA \: of \: outer \: surface \: of \: pipe =$

$= \: 2\pi \: r _{2} h$

$= \: (2 \: \times \: \frac{22}{7} \: \times \: 2 \: \times \: 77) \: cm {}^{2}$

$= \: (22 \: \times \: 22 \: \times \: 2.2 \: \times )$

$= \: 1064.8 \: cm {}^{2}$

$(iii) Total \: surface \: area \: of \: pipe \: = \: CSA \: of \: inner \: surface \: + \: CSA \: of \: outer \: surface \: + \: Area \: of \: both \: circular \: ends \: of \: pipe.$

$= 2\pi \: r _{1} h \: + \: 2\pi \: r _{2} h \: + \: 2\pi \: (r {}^{2} _{2} \: - r {}^{2} _{1})$

$= [\: 968 \: + \: 1064.8 \: + \: 2\pi \: (2.2) {}^{2} - (2) {}^{2} \: cm {}^{2} ]$

$= \: (2032.8 \: + \: 2 \: \times \: \frac{22}{7} \: \times \: 0.84)cm {}^{2}$

$= \: (2032.8 \: + \: 5.28)cm {}^{2}$

$= \: 2038.8 \: cm {}^{2}$

$☘Therefore \: the \: total \: surface \: area \: \\ of \: the \: cylindrical \: pipe \: is \: 2038.8 \: cm {}^{2}$