The given figure shows a metal pipe 77 cm long. The inner diameter of a cross-section is 4 cm and the outer one is 4.4 cm. Find its
(i) inner curved surface area
(ii) outer curved surface area
(iii) total surface area.
The given figure shows a metal pipe 77 cm long. The inner diameter of a cross-section is 4 cm and the outer one is 4.4 cm. Find its
(i) inner curved surface area
(ii) outer curved surface area
(iii) total surface area.

Solution:

Given height of the metal pipe = 77 cm

Inner diameter = 4 cm

Inner radius, r = d/2 = 4/2 = 2 cm

Outer diameter = 4.4 cm

Outer radius, R = d/2 = 4.4/2 = 2.2 cm

(i)Inner curved surface area = 2rh

= 2×(22/7)×2×77

= 968 cm2

Hence the inner surface area is 968 cm2.

(ii)Outer curved surface area = 2Rh

= 2×(22/7)×2.2×77

= 1064.8 cm2

Hence the outer curved surface area is 968 cm2.

(iii)Area of ring = (R2-r2)

= (22/7)×(2.22-22)

= (22/7)×(4.84-4)

= (22/7)×0.84

= 2.64

Total surface area = inner surface area + outer surface area + area of two rings

= 968+ 1064.8+ 2×2.64

= 2038.08 cm2

Hence the total surface area of the metal pipe is 2038.08 cm2.