a metal pipe is 66cm long. the inner diametre of a cross section is 3cm, the outer diametre being 3.3cm.find its inner SA, outer SA, total SA
Answers
Answer:
Step-by-step explanation:
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Answer:
Inner curved surface area = 621.72 cm²
Outer curved surface area = 683.892 cm²
Total surface area = 1308.582 cm²
Step-by-step explanation:
Given:
- Length of metal pipe = 66 cm
- The inner diameter = 3 cm
- The outer diameter = 3.3 cm
To Find:
- Inner surface area
- Outer surface area
- Total surface area
Solution:
Inner Surface area:
First let us find the inner surface area of the metal pipe.
Here the metal pipe is in the form of a hollow cylinder.
Hence we have to find the curved surface area of the cylinder
The CSA of a cylinder is given by,
CSA of a cylinder = 2 π r h
where r = radius
h = height of the cylinder
The radius of inner area = 3/2 = 1.5 cm
Substituting the data,
CSA of inner cylinder = 2 × 3.14 × 1.5 × 66
CSA of inner cylinder = 621.72 cm²
Hence the inner curved surface area is 621.72 cm².
Outer surface area:
Now we have to find the outer surface area of the metal pipe.
CSA of outer cylinder = 2 × π × r × h
Radius of outer cylinder = 3.3/2 = 1.65 cm
Substitute the data,
CSA of outer cylinder = 2 × 3.14 × 1.65 × 66
CSA of outer cylinder = 683.892 cm²
Hence the outer curved surface area is 683.892 cm².
Total surface area:
The total surface area of the pipe is given by,
Total surface area of pipe = Outer CSA + Inner CSA + Area of 2 bases
Now,
Area of base = Outer base - Inner base
Area of base = 3.14 × 1.65² - 3.14 × 1.5²
Area of base = 8.55 - 7.065
Area of base = 1.485 cm²
Substitute the data,
Total surface area = 683.892 + 621.72 + 2 × 1.485
Total surface area = 1305.612 + 2.97
Total surface area = 1308. 582 cm²
Hence the total surface area of the cylinder is 1308.582 cm².