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

Here, h = 77 cm, 

Outer radius (R) = 4. 4/ 2 cm = 2.2 cm, 

Inner radius (r) = 4/ 2 cm = 2 cm 

(i) Inner curved surface area of the pipe 

= 2πrh 

= 2 × 22/ 7 × 2 × 77 cm² 

= 2 × 22 × 22 cm² = 968 cm² Ans.

(ii) Outer curved surface area of the pipe = 2πRh 

= 2 × 22/ 7 × 2.2 × 77 cm² = 44 × 24.2 cm² 

= 1064.80 cm² Ans. 

(iii) Total surface area of the pipe = inner curved surface area + outer 

curved surface area + areas of the two base rings. 

= 2πrh + 2πRh + 2π (R² – r²) 

= 968 cm² + 1064.80 cm² + 2 × 22/ 7 [(2.2)² – 22] cm² 

= 2032.80 cm² + 5.28 cm² = 2038.08 cm² Ans