A metal pipe is 77cm long. The inner diameter of a cross section is 4cm, the outer diameter being 4.4 cm. Find its inner curved surface area. outer curved surface area. total surface area.

Explanation

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'
iii) The total surface area of the pipe can be obtained by adding the inner and outer curved surface areas along with the area of both the circular ends.
We can find the area of circular ends by subtracting the area of the inner circle from the outer circle area.
Area of both the circular ends of the pipe = '2 π (R² - r²)'
TSA of pipe = CSA of inner surface + CSA of outer surface + Area of both the circular ends of the pipe
Hence, TSA of the pipe = '2πrh + 2πRh + 2π(R² -r²)'
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'`
Total surface area = `'2πrh + 2πRh + 2π (R² - r²)'
= '968 cm² + 1064.8 cm² + 5.28 cm²'`
[Since, Inner curved surface area = 968 cm², Outer curved surface area = '`1064.8 cm²]`
= `2038.08 cm²'`