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

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A metal pipe is 77 cm long. The inner diameter of a cross section is 4 cm, the outer diameter being 4.4 cm.(See the given figure)

(i) inner curved surface area,

(ii) outer curved surface area,

(iii) total surface area.

`["Assume "pi=22/7]`

 

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Solution

Inner radius (r1) of cylindrical pipe = (4/2)cm = 2cm

Outer radius (r2) of cylindrical pipe = (4.4/2)cm = 2.2cm

Height (h) of cylindrical pipe = Length of cylindrical pipe = 77 cm

 

(i) CSA of inner surface of pipe`= 2pir_1h`

                                            `=(2xx22/7xx2xx77)cm^2`

                                            `=968cm^2`

 

(ii) CSA of outer surface of pipe`= 2pir_2h`

                                             `=(2xx22/7xx2xx77)cm^2`

                                             `=(22xx22xx2.2)cm^2`

                                             `=1064.8cm^2`

 

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

                                          `=2pir_1h + 2pir_2h + 2pi(r_2^2 - r_1^2)`

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

                                          `=(2032.8 + 2xx22/7xx0.84)cm^2`

                                          `=(2032.8 + 5.28)cm^2`

                                          `=2038.08cm^2`

Therefore, the total surface area of the cylindrical pipe is 2038.08 cm2.

Concept: Surface Area of Cylinder
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APPEARS IN

NCERT Class 9 Maths
Chapter 13 Surface Area and Volumes
Exercise 13.2 | Q 3 | Page 216

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