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. 13.11). Find its

 

(i) inner curved surface area,

(ii) outer curved surface area

(iii) total surface area

(Assume π=22/7)

Solution:

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.