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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. Select the statements that hold true.

[Assume π=227]


A

Inner curved surface area =968 cm2

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B

Outer curved surface area =1064.8 cm2

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C

Total surface area =2038.08 cm2

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D

Total surface area =6758.08 cm2

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Solution

The correct options are
A

Inner curved surface area =968 cm2


B

Outer curved surface area =1064.8 cm2


C

Total surface area =2038.08 cm2


Inner radius (r1) of the cylindrical pipe =[42]cm=2 cm
outer radius (r2) of cylindrical pipe
=[4.42]cm=2.2 cm
Height (h) of cylindrical pipe = length of cylindrical pipe = 77 cm
CSA of inner surface of pipe = 2πr1h
=[2×227×2×77]cm2
=968 cm2
CSA of outer surface of pipe = 2πr2h
=[2×227×2.2×77]cm2
(22×22×2.2)cm2
=1064.8 cm2
Total surface area of pipe = CSA inner surface + CSA of outer surface + Area of both circular ends of pipe.
=2πr1h+2πr2h+2π(r22r21)=[9668+1064.8+2π{(2.2)2(2)2}]cm2=(2032.8+5.28)cm2=2038.08 cm2
Therefore, the total surface area of the cylindrical pipe is 2038.08 cm2.


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