Question

$\large{\underline{\underline{\maltese{\orange{\pmb{\sf{ \; Question \; :- }}}}}}}$

A metal pipe is 77 cm long. The inner diameter of a cross section is 4 cm, the outer diameter being 4.4 cm. Find :-


(i) Inner Curved Surface Area .
(ii) Outer Curved Surface Area.
(iii) Total Surface Area .


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$\large{\underline{\underline{\maltese{\orange{\pmb{\sf{ \; Note \; :- }}}}}}}$

$\longmapsto$ Answer with proper explaination will be appreciated .
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Answer 1

Step-by-step explanation:

Solution

(i)Inner Covered Surface Area

According to the question inner diameter is 4 cm,

Then,

Inner radius of a cylindrical pipe =r1=

$\sf{\frac{inner \: diameter}{2 } = \big(\frac{ 4}{2} \big)cm = 2cm}$

Height (h) of cylindrical pipe=77 cm,

Curved Surface Area of inner surface of pipe  =2πr1h

${ \longmapsto{ \sf{= \bigg \lgroup(2×722×2×77 \bigg \rgroup)cm2}}}$

${ \dashrightarrow{ \sf{ \boxed{ \sf \orange{ \underline{=968cm2}}}}}}$

(ii) Outer Curved Surface Area.

According to the question outer diameter is 4.4 cm

$\sf{\frac{outer \: diameter}{2 } = \big(\frac{ 4.4}{2} \big)cm = 2.2cm}$

• Outer radius of cylindrical pipe =r2=

• Height of cylinder = h = 77 cm,

• Curved area of outer surface of pipe = 2πr2h

${ \longmapsto{ \sf{= \bigg\lgroup(=(2×722×2.2×77)cm2\bigg \rgroup)cm2}}}$

${ \longmapsto{ \sf{=\bigg\lgroup=(2×22×2.2×11)cm2)cm2\bigg \rgroup)cm2}}}$

${ \dashrightarrow{ \sf{ \boxed{ \sf\pink{ \underline{=1064.8cm {}^{2} }}}}}}$

(iii)Total Surface Area

${ \dashrightarrow{ \sf{ \boxed{ \sf \red{ \underline{=2039.08cm {}^{2} }}}}}}$

For Explanation See Attachment

Answer 2

$\large{\underline{\underline{\maltese{\orange{\pmb{\sf{ \; Question \; :- }}}}}}}$

A metal pipe is 77 cm long. The inner diameter of a cross section is 4 cm, the outer diameter being 4.4 cm. Find :-

• Inner Curved Surface Area .
• Outer Curved Surface Area.
• Total Surface Area .

$\large{\underline{\underline{\maltese{\orange{\pmb{\sf{ \; GIVEN \; :- }}}}}}}$

• HEIGHT OF THE METAL PIPE IS 77 cm long.

• INNER DIAMETER = 4 cm.

• OUTER DIAMETER = 4.4 cm.

$\large{\underline{\underline{\maltese{\orange{\pmb{\sf{ \; TO \: FIND \; :- }}}}}}}$

• Inner Curved Surface Area .

• Outer Curved Surface Area.

• Total Surface Area .

$\large{\underline{\underline{\maltese{\orange{\pmb{\sf{ \; SOLUTION \; :- }}}}}}}$

• INNER CURVED SURFACE AREA.

FORMULA USED FOR FINDING INNER SURFACE AREA OF THE PIPE :-

${r}^{1} = \frac{inner \: diameter }{2} = (\frac{4}{2})cm = 2cm$

$⇒( \frac{4}{2} ) \: cm = 2 \: cm$

FORMULA USED FOR FINDING CURVED SURFACE AREA OF INNER SURFACE OF THE PIPE :-

• 2πr¹h

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

$⇒968 \: {cm}^{2}$

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• OUTER CURVED SURFACE AREA.

FORMULA USED FOR FINDING OUTER SURFACE AREA OF THE PIPE :-

${r}^{2} = \frac{outer \: diamterer }{2}$

$= (\frac{4.4}{2})cm = 2.2 \: cm$

FORMULA USED FOR FINDING CURVED SURFACE AREA OF OUTER SURFACE OF THE PIPE :-

• 2πr²h

$⇒(2 \times \frac{22}{7} \times 2.2 \times 77 ){cm}^{2}$

$⇒(2 \times 22 \times 2.2 \times 11) \: {cm}^{2}$

$⇒1064.8 \: {cm}^{2}$

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• TOTAL SURFACE AREA.

WE KNOW;

Total surface area = curved surface area of inner cylinder + curved surface of outer cylinder + 2 × Area of base

Total surface area = curved surface area of inner cylinder + curved surface of outer cylinder + 2 × Area of baseArea of base = area of circle with radius 2.2 cm - Area of circle with radius 2 cm

⇒ πr²^2 - πr¹^2

⇒ 22 × ((2.2)² - (2)²)

⇒ 22/7 × (4.84 - 4)

⇒ 22/7 × (0.84)

⇒ 2.74 cm²

Total surface area = curved surface area of inner cylinder + curved surface area of outer cylinder + 2 × Area of base

• ⇒ (968 + 1064.8 + 2 × 2.74) cm²

• ⇒ (2032.8 + 5.76) cm²

• ⇒ 2039.08 cm²

Therefore, the total surface area of the cylindrical pipe is 2039.08 cm².

$\large{\underline{\underline{\maltese{\orange{\pmb{\sf{ \; Answer \; :- }}}}}}}$

• INNER CURVED SURFACE AREA = 968 cm².

• OUTER CURVED SURFACE AREA = 1064.8 cm².

• TOTAL SURFACE AREA = 2039.08 cm².