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...(i) find its inner curved surface area (ii) outer curved surface area (iii) total surface area .

No spamming pls....​

Answer 1

Step-by-step explanation:

Inner Surface area of the Pipe = 968 Square cm.

Outer Surface area of the pipe = 1064.8 Square cm.

Total Surface Area = = 2038.08 Square cm.

Step-by-step explanation:

A pipe will have two layers as shown in picture.  

There is a inner Cylinder and Outer Cylinder.

Inner Radius = Inner Diameter / 2 = 4 / 2 = 2 cm = r

Outer Radius = Outer Diameter / 2 = 4.4/2 = 2.2 cm = R

Height of the pipe = 77 cm = h

Inner Surface area of the Pipe = 2∏rh = 2*22*2*77/7 = 968 Square cm.

Outer Surface area of the pipe = 2∏Rh = 2*22*2.2*77/7 = 1064.8 Square cm.

Total Surface area = Inner Surface area + Outer Surface area + 2 * Cross section surface area.  

The cross section suface area is present at two ends of the pipe.  

This is the area covered between 2 circles.  

Total Surface area = Inner Surface area + Outer Surface area + 2 * Cross section surface area.  

= 968 + 1064.8 + 2*∏(R^2 – r^2)

= 2032.8 + 2*22*(2.2*2.2 – 2*2)/7

= 2032.8 + 5.28

= 2038.08 Square cm.

.

Answer 2

$\huge{ \mathtt{Given: }}$

Inner diameter of a cross section=4cm

therefore, inner radius (r)=2cm

Given, length of metal pipe (l)=77cm

$\large{(Inner )\: CSA\: of \: cylinder = 2\pi \: rh} \\ { = > 2 \times \frac{22}{7} \times 2 \times 77} \\ = > 44 \times 22 {cm}^{2} \\ = > 968 {cm}^{2}$

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$\huge{ \mathtt{Given:}}$

Outer diameter=4.4cm

therefore, outer radius (R)=2.2cm

Given,length of metal pipe (l)=77cm

$\large{ =>(Outer) \: CSA = 2\pi \: Rh} \\ = > 2 \times \frac{22}{7} \times 2.2 \times 77 \\ = > 44 \times 24.2 {cm}^{2} \\ = > 1064.8 {cm}^{2}$

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$\huge{ \mathtt{Total \: surface \: area}}$

Total surface area=inner surface area+outer surface area+area of the base rings

$= > 2\pi \: rh + 2\pi \: Rh + 2\pi( {R}^{2} - {r}^{2} ) \\ = > 1064.8 + 968 + 2 \times \frac{22}{7} ( {22}^{2} - {2}^{2} ) \\ = > 2032.8 + \frac{44}{7} (4.844) \\ = > 2032.8 + \frac{44}{7} \times 0.84 \\ = > 2038.08 {cm}^{2}$

Therefore,the answers are-

$\small{\boxed{ \mathtt{ \pink{Inner \: curved \: surface \: area = 968 {cm}^{2} }}}}$

$\small{\boxed{ \mathtt{ \green{Outer \: curved \: surface \: area = 1064.8 {cm}^{2} }}}}$

$\small{\boxed{ \mathtt{ \blue{ Total \: surface \: area = 203.08 {cm}^{2}}}}}$

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$\large{ \mathtt{ \red{Thanks...♡ }}}$