A metal pipe is 77 cm long. The inner diameter of a cross-section is 4 cm, the outer diameter being 4.4cm. (see fig.). Find its
(i) inner curved surface area,
(ii) outer curved surface area
(iii) total surface area
(Assume π=22/7)
Let r1 and r2 Inner and outer radii of cylindrical pipe
r1 = 4/2 cm = 2 cm
r2 = 4.4/2 cm = 2.2 cm
Height of cylindrical pipe,
h = length of cylindrical pipe = 77 cm
(i) curved surface area of outer surface of pipe = 2πr1h
= 2 × (22/7) × 2 × 77 cm2
= 968 cm2
(ii) curved surface area of outer surface of pipe
= 2πr2h
= 2 × (22/7) × 2.2 × 77 cm2
= (22 × 22 × 2.2) cm2
= 1064.8 cm2
(iii) Total surface area of pipe = inner curved surface area+ outer curved surface area+ Area of both circular ends of pipe.
= 2r1h + 2r2h + 2π(r12-r22)
= 9668 + 1064.8 + 2 × (22/7) × (2.22-22)
= 2031.8 + 5.28
= 2038.08 cm2
Therefore, the total surface area of the cylindrical pipe is 2038.08 cm2.