The outer diameter of a pipe is 70 cm and it is 21 m long. Find the cost of painting the outer surface of the pipe at the rate of 10 per square metre. 22. rbruerto
Answers
Answer:
The inner radius, outer radius, and height of the cylinder are r, R, and h respectively.
Inner curved surface area = 2πrh
Outer curved surface area = 2πRh
Length of the pipe, h = 77 cm
Inner radius(r) of the pipe and outer radius(R) of the pipe are:
r = 4/2 cm = 2 cm
R = 4.4/2 cm = 2.2 cm
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
Step-by-step explanation:
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