Question 3 ex 13 .2 chapter …

3. 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+(r₁²-r₂²)

= 9668+1064.8+2(2.2²-2²)

= 2031.8+5.28

= 2038.08 cm²

Therefore, the total surface area of the cylindrical pipe is 2038.08 cm².