Question

A metal pipe is 77 cm. long. The inner diameter of a cross section is 4 cm., the outer diameter being 4.4 cm. (see figure) Find its
(i) inner curved surface area
(ii) outer curved surface area
(iii) Total surface area

Answer 1

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Answer 2

Answer:

(i) 968 cm²

(ii) 1064.8 cm²

(iii) 2038.08 cm²

Step-by-step explanation:

(i)The inner circumference of the pipe=2πr =2×(22/7)×2=12.57 cm.

{Given that 4 cm is the inner diameter i.e. inner radius = 2 cm}

Hence, the inner curved area = (2πr)L=12.57×77=968 cm² (Answer)

{Given also that the length of the pipe is 77 cm.}

(ii) The outer circumference of the pipe=2πR =2×(22/7)×2.2=13.828 cm.

{Given that 4.4 cm is the outer diameter i.e. outer radius = 2.2 cm}

Hence, the outer curved area = (2πR)L=13.828×77=1064.8 cm² (Answer)

{Given also that the length of the pipe is 77 cm.}

(iii) Now the total surface area of the pipe is given by

(2πr)L+(2πR)L+2π(R²-r²) {Since, the side surface area on one side is π(R²-r²)}

= 968+1064.8+2(22/7)(2.2²-2²)

=2032.8 + 5.28

= 2038.08 cm². (Answer)