Question 3 A metal pipe is 77 cm long. The inner diameter of a cross-section is 4 cm, the outer diameter being 4.4 cm. Find its, (i) Inner curved surface area (ii) Outer curved surface area (iii) Total surface area. [Assumeπ=227]
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Solution
Inner radius (r1) of the cylindrical pipe =[42]cm=2cm outer radius (r2) of cylindrical pipe =[4.42]cm=2.2cm Height (h) of cylindrical pipe = length of cylindrical pipe = 77 cm CSA of inner surface of pipe = 2πr1h =[2×227×2×77]cm2 =968cm2 CSA of outer surface of pipe = 2πr2h =[2×227×2.2×77]cm2 (22×22×2.2)cm2 =1064.8cm2 Total surface area of pipe = CSA inner surface + CSA of outer surface + Area of both circular ends of pipe. =2πr1h+2πr2h+2π(r22−r21)=[9668+1064.8+2π{(2.2)2−(2)2}]cm2=(2032.8+5.28)cm2=2038.08cm2 Therefore, the total surface area of the cylindrical pipe is 2038.08cm2.