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The volume of a metallic pipe is 1408 cm3. Its length is 14 cm and its internal radius is 7 cm. What is the thickness of the pipe?
- a)3 cm
- b)4 cm
- c)2 cm
- d)2.5 cm
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The volume of a metallic pipe is 1408 cm3. Its length is 14 cm and its...
To find the thickness of the pipe, we need to subtract the internal radius from the external radius of the pipe.
Given:
Volume of the pipe = 1408 cm^3
Length of the pipe = 14 cm
Internal radius = 7 cm
Let's assume the external radius of the pipe is r cm.
1. Finding the external radius:
Since the pipe is cylindrical, we can use the formula for the volume of a cylinder to find the external radius.
Volume of a cylinder = π * r^2 * h
Given: Volume = 1408 cm^3, Height = 14 cm
1408 = π * r^2 * 14
Dividing both sides by 14π, we get:
r^2 = 1408 / (14π)
r^2 = 32 / π
Taking the square root of both sides, we get:
r = √(32 / π)
2. Finding the thickness:
The thickness of the pipe is the difference between the external radius and the internal radius.
Thickness = External radius - Internal radius
Thickness = (√(32 / π)) - 7
3. Simplifying the expression:
To simplify the expression, we need to rationalize the denominator.
Multiplying the numerator and denominator by π, we get:
Thickness = (√(32 / π)) - 7 * (√(π / π))
Thickness = (√(32π / π^2)) - 7√(π / π)
Simplifying further:
Thickness = (4√π / π) - 7
Therefore, the thickness of the pipe is 4 cm, which is option (c).
Given:
Volume of the pipe = 1408 cm^3
Length of the pipe = 14 cm
Internal radius = 7 cm
Let's assume the external radius of the pipe is r cm.
1. Finding the external radius:
Since the pipe is cylindrical, we can use the formula for the volume of a cylinder to find the external radius.
Volume of a cylinder = π * r^2 * h
Given: Volume = 1408 cm^3, Height = 14 cm
1408 = π * r^2 * 14
Dividing both sides by 14π, we get:
r^2 = 1408 / (14π)
r^2 = 32 / π
Taking the square root of both sides, we get:
r = √(32 / π)
2. Finding the thickness:
The thickness of the pipe is the difference between the external radius and the internal radius.
Thickness = External radius - Internal radius
Thickness = (√(32 / π)) - 7
3. Simplifying the expression:
To simplify the expression, we need to rationalize the denominator.
Multiplying the numerator and denominator by π, we get:
Thickness = (√(32 / π)) - 7 * (√(π / π))
Thickness = (√(32π / π^2)) - 7√(π / π)
Simplifying further:
Thickness = (4√π / π) - 7
Therefore, the thickness of the pipe is 4 cm, which is option (c).
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The volume of a metallic pipe is 1408 cm3. Its length is 14 cm and its...
Because 14cm /7cm is 2cm
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