The hollow metal pipe is 63 cm long. The inner diameter of cross-section is 4 cm and the outer diameter is 4.8 cm. Find the total surface area of the pipe.

Sub Grade: 9

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1734.46 cm2

1834.43 cm2

1834.46 cm2

1537.48 cm2

answer is A.

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Detailed Solution

Length = 63 cm , or we can say height =63 cm
Inner diameter= 4cm   , outer diameter = 4 .8 cm
Inner diameter of crossetion = inner diameter /2 = 4/2 = 2
Let it be r = 2 cm
Similarly outer radius be R
R = 4.8 / 2 = 2.4 cm
Total sufacaae of hollow pipe = curved surface area of inner cylindrical part + curved surface area of outer cylindrical part + area of the two circular ends
Area of circular ends = area of outer circle - area of inner circle
π R2- π r2
π ( R2- r2)
Substituting volume of R and r
π ( 2.4 )2 - (2)2 )
π (1. 76 )cm2    Area of 2 circular lease= 2X 1.76 π cm2 = 3.52 π cm2
Curved surface area = 2 π radius X radius X height
Curved surface area of outer circle = 2π Rh = 2 x π X2.4 x63 = 302.45 π cm2 Curved surface area of inner circle = 2π Rh = 2 x π x 2 x 63 = 252 π cm2   On substituting (1)(2) and (3)
Total surface area= 252 π+ 302.45 π+ 3.52 π
= 557.92 π
=557.92 x 3.14 = 1734.46 cm2

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