Question

A metal pipe is 77 cm long, the inner diameter of the cross-section is 4 cm and the outer diameter is Find the (i) inner curved surface area (ii) outer curved surface area (iii) total surface area.

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Answer 1

Answer:

Let the inner radius, outer radius, and height of the cylinder are r, R, and h respectively.

r = 4/2 cm = 2 cm

R = 4.4/2 cm = 2.2 cm

Length of the pipe, h = 77 cm

Inner radius(r) of the pipe and outer radius(R) of the pipe are:

i) Inner curved surface area = 2πrh

= 2 × 22/7 × 2 cm × 77 cm

= 968 cm²

ii) Outer curved surface area = 2πRh

= 2 × 22/7 × 2.2 cm × 77 cm

= 1064.8 cm²

Now, area of both the circular ends of the pipe

= 2π(R² - r²)

= 2 × 22/7 × [(2.2 cm)² - (2 cm)²]

= 2 × 22/7 × [4.84 cm² - 4 cm²]

= 2 × 22/7 × 0.84 cm²

= 5.28 cm²

iii) Total surface area 

= 2πrh + 2πRh + 2π (R² - r²)

= 968 cm² + 1064.8 cm² + 5.28 cm² 

=2038.08 cm²