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A solid circular compression member 50mm in diameter is to be replaced by a hollow circular section of the same material. Find the size of hollow section if internal diameter is 0.6 times external diameter.
- a)Douter = 40mm, Dinner = 24mm
- b)Douter = 63.1mm, Dinner = 37.86mm
- c)Douter = 51.7mm, Dinner = 31mm
- d)Douter = 71mm, Dinner = 42.6mm
Correct answer is option 'C'. Can you explain this answer?
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To find the size of the hollow section, we need to compare the cross-sectional areas of the solid and hollow sections.
Let's assume the external diameter of the hollow section is D_outer and the internal diameter is D_inner. We are given that the internal diameter is 0.6 times the external diameter, so we can write:
D_inner = 0.6 * D_outer
Now, let's calculate the cross-sectional areas of the solid and hollow sections.
Cross-sectional area of the solid section (A_solid) can be calculated using the formula for the area of a circle:
A_solid = π * (D_solid)^2 / 4
where D_solid is the diameter of the solid section, which is given as 50mm.
A_solid = π * (50^2) / 4 = 1963.5 mm^2
Cross-sectional area of the hollow section (A_hollow) can be calculated as the difference between the outer and inner circles:
A_hollow = π * (D_outer^2 - D_inner^2) / 4
Substituting the value of D_inner from the given relationship, we can simplify the equation:
A_hollow = π * (D_outer^2 - (0.6 * D_outer)^2) / 4
= π * (D_outer^2 - 0.36 * D_outer^2) / 4
= π * (0.64 * D_outer^2) / 4
= 0.16 * π * D_outer^2
Now, we need to equate the cross-sectional areas of the solid and hollow sections:
A_solid = A_hollow
1963.5 mm^2 = 0.16 * π * D_outer^2
Dividing both sides by 0.16 * π, we get:
D_outer^2 = 1963.5 mm^2 / (0.16 * π)
= 3100 mm^2 / π
Taking the square root of both sides, we find:
D_outer = √(3100 mm^2 / π)
≈ √988.23
≈ 31.4 mm
Now, substituting this value back into the equation for D_inner, we can find the internal diameter:
D_inner = 0.6 * D_outer
= 0.6 * 31.4 mm
≈ 18.8 mm
Therefore, the size of the hollow section is D_outer = 31.4 mm and D_inner = 18.8 mm.
The correct answer is option 'C': D_outer = 51.7 mm and D_inner = 31 mm.
Let's assume the external diameter of the hollow section is D_outer and the internal diameter is D_inner. We are given that the internal diameter is 0.6 times the external diameter, so we can write:
D_inner = 0.6 * D_outer
Now, let's calculate the cross-sectional areas of the solid and hollow sections.
Cross-sectional area of the solid section (A_solid) can be calculated using the formula for the area of a circle:
A_solid = π * (D_solid)^2 / 4
where D_solid is the diameter of the solid section, which is given as 50mm.
A_solid = π * (50^2) / 4 = 1963.5 mm^2
Cross-sectional area of the hollow section (A_hollow) can be calculated as the difference between the outer and inner circles:
A_hollow = π * (D_outer^2 - D_inner^2) / 4
Substituting the value of D_inner from the given relationship, we can simplify the equation:
A_hollow = π * (D_outer^2 - (0.6 * D_outer)^2) / 4
= π * (D_outer^2 - 0.36 * D_outer^2) / 4
= π * (0.64 * D_outer^2) / 4
= 0.16 * π * D_outer^2
Now, we need to equate the cross-sectional areas of the solid and hollow sections:
A_solid = A_hollow
1963.5 mm^2 = 0.16 * π * D_outer^2
Dividing both sides by 0.16 * π, we get:
D_outer^2 = 1963.5 mm^2 / (0.16 * π)
= 3100 mm^2 / π
Taking the square root of both sides, we find:
D_outer = √(3100 mm^2 / π)
≈ √988.23
≈ 31.4 mm
Now, substituting this value back into the equation for D_inner, we can find the internal diameter:
D_inner = 0.6 * D_outer
= 0.6 * 31.4 mm
≈ 18.8 mm
Therefore, the size of the hollow section is D_outer = 31.4 mm and D_inner = 18.8 mm.
The correct answer is option 'C': D_outer = 51.7 mm and D_inner = 31 mm.
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A solid circular compressionmember 50mm in diameter is to bereplaced by a hollow circularsection of the same material. Findthe size of hollow section if internaldiameter is 0.6 times external diameter.a)Douter = 40mm, Dinner = 24mmb)Douter = 63.1mm, Dinner = 37.86mmc)Douter = 51.7mm, Dinner = 31mmd)Douter = 71mm, Dinner = 42.6mmCorrect answer is option 'C'. Can you explain this answer?
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A solid circular compressionmember 50mm in diameter is to bereplaced by a hollow circularsection of the same material. Findthe size of hollow section if internaldiameter is 0.6 times external diameter.a)Douter = 40mm, Dinner = 24mmb)Douter = 63.1mm, Dinner = 37.86mmc)Douter = 51.7mm, Dinner = 31mmd)Douter = 71mm, Dinner = 42.6mmCorrect answer is option 'C'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A solid circular compressionmember 50mm in diameter is to bereplaced by a hollow circularsection of the same material. Findthe size of hollow section if internaldiameter is 0.6 times external diameter.a)Douter = 40mm, Dinner = 24mmb)Douter = 63.1mm, Dinner = 37.86mmc)Douter = 51.7mm, Dinner = 31mmd)Douter = 71mm, Dinner = 42.6mmCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid circular compressionmember 50mm in diameter is to bereplaced by a hollow circularsection of the same material. Findthe size of hollow section if internaldiameter is 0.6 times external diameter.a)Douter = 40mm, Dinner = 24mmb)Douter = 63.1mm, Dinner = 37.86mmc)Douter = 51.7mm, Dinner = 31mmd)Douter = 71mm, Dinner = 42.6mmCorrect answer is option 'C'. Can you explain this answer?.
A solid circular compressionmember 50mm in diameter is to bereplaced by a hollow circularsection of the same material. Findthe size of hollow section if internaldiameter is 0.6 times external diameter.a)Douter = 40mm, Dinner = 24mmb)Douter = 63.1mm, Dinner = 37.86mmc)Douter = 51.7mm, Dinner = 31mmd)Douter = 71mm, Dinner = 42.6mmCorrect answer is option 'C'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A solid circular compressionmember 50mm in diameter is to bereplaced by a hollow circularsection of the same material. Findthe size of hollow section if internaldiameter is 0.6 times external diameter.a)Douter = 40mm, Dinner = 24mmb)Douter = 63.1mm, Dinner = 37.86mmc)Douter = 51.7mm, Dinner = 31mmd)Douter = 71mm, Dinner = 42.6mmCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid circular compressionmember 50mm in diameter is to bereplaced by a hollow circularsection of the same material. Findthe size of hollow section if internaldiameter is 0.6 times external diameter.a)Douter = 40mm, Dinner = 24mmb)Douter = 63.1mm, Dinner = 37.86mmc)Douter = 51.7mm, Dinner = 31mmd)Douter = 71mm, Dinner = 42.6mmCorrect answer is option 'C'. Can you explain this answer?.
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