# 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

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]

#### 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