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 Fig. 13.11). Find its
i) Inner curved surface area,
ii) Outer curved surface area,
iii) Total surface area.
Solution:
Let's construct the diagram according to the given question.
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
☛ Check: NCERT Solutions Class 9 Maths Chapter 13
Video Solution:
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 Fig. 13.11). Find its i) Inner curved surface area ii) Outer curved surface area iii) Total surface area
Class 9 Maths NCERT Solutions Chapter 13 Exercise 13.2 Question 3
Summary:
It is given that there is a metal pipe that is 77 cm long. The inner diameter of a cross section is 4 cm, the outer diameter is 4.4 cm. We have found that Inner curved surface area = 968 cm², Outer curved surface area = 1064.8 cm² and the Total surface area = 2038.08 cm².
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