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A cubic casting of 50 mm side under goes volumetric solidification shrinkage and volumetric solid contraction of 4% and 6% respectively. No riser is used. Assume uniform cooling in all directions. The side of the cube after solidification and contraction is
[ME 2011]
- a)48.32 mm
- b)49.90 mm
- c)49.94 mm
- d)49.96 mm
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
A cubic casting of 50 mm side under goes volumetric solidification shr...
Given:
- Side of the cubic casting = 50 mm
- Volumetric solidification shrinkage = 4%
- Volumetric solid contraction = 6%
- No riser is used
To find:
The side of the cube after solidification and contraction.
Assumptions:
- Uniform cooling in all directions
- No other factors affecting the final size of the casting
Solution:
Step 1: Calculating the volume of the cube before solidification and contraction
The volume of a cube can be calculated using the formula:
Volume = (Side)^3
Given that the side of the cube is 50 mm, we can calculate the volume as follows:
Volume_before = (50 mm)^3
Volume_before = 125,000 mm^3
Step 2: Calculating the volume after solidification shrinkage
Solidification shrinkage refers to the reduction in volume that occurs as the material changes from a liquid to a solid state. In this case, the shrinkage is given as 4% of the original volume.
We can calculate the volume after solidification shrinkage as follows:
Volume_after_solidification = Volume_before - (4% of Volume_before)
Volume_after_solidification = 125,000 mm^3 - (0.04 * 125,000 mm^3)
Volume_after_solidification = 125,000 mm^3 - 5,000 mm^3
Volume_after_solidification = 120,000 mm^3
Step 3: Calculating the volume after solid contraction
Solid contraction refers to the reduction in volume that occurs as the material cools and solidifies further. In this case, the contraction is given as 6% of the volume after solidification.
We can calculate the volume after solid contraction as follows:
Volume_after_contraction = Volume_after_solidification - (6% of Volume_after_solidification)
Volume_after_contraction = 120,000 mm^3 - (0.06 * 120,000 mm^3)
Volume_after_contraction = 120,000 mm^3 - 7,200 mm^3
Volume_after_contraction = 112,800 mm^3
Step 4: Calculating the side of the cube after solidification and contraction
The side of the cube after solidification and contraction can be calculated by taking the cube root of the volume after contraction.
Side_after = (Volume_after_contraction)^(1/3)
Side_after = (112,800 mm^3)^(1/3)
Side_after ≈ 48.32 mm
Conclusion:
The side of the cube after solidification and contraction is approximately 48.32 mm. Therefore, the correct answer is option A.
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Community Answer
A cubic casting of 50 mm side under goes volumetric solidification shr...
Side of cube after solidification
(
0.96×(50)3)1/3 = 49.32mmSide of cube after contraction
(0.94×(49.32)3)1/3 = 48.32mm
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A cubic casting of 50 mm side under goes volumetric solidification shrinkage and volumetric solid contraction of 4% and 6% respectively. No riser is used. Assume uniform cooling in all directions. The side of the cube after solidification and contraction is[ME 2011]a)48.32 mmb)49.90 mmc)49.94 mmd)49.96 mmCorrect answer is option 'A'. Can you explain this answer?
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A cubic casting of 50 mm side under goes volumetric solidification shrinkage and volumetric solid contraction of 4% and 6% respectively. No riser is used. Assume uniform cooling in all directions. The side of the cube after solidification and contraction is[ME 2011]a)48.32 mmb)49.90 mmc)49.94 mmd)49.96 mmCorrect answer is option 'A'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A cubic casting of 50 mm side under goes volumetric solidification shrinkage and volumetric solid contraction of 4% and 6% respectively. No riser is used. Assume uniform cooling in all directions. The side of the cube after solidification and contraction is[ME 2011]a)48.32 mmb)49.90 mmc)49.94 mmd)49.96 mmCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cubic casting of 50 mm side under goes volumetric solidification shrinkage and volumetric solid contraction of 4% and 6% respectively. No riser is used. Assume uniform cooling in all directions. The side of the cube after solidification and contraction is[ME 2011]a)48.32 mmb)49.90 mmc)49.94 mmd)49.96 mmCorrect answer is option 'A'. Can you explain this answer?.
A cubic casting of 50 mm side under goes volumetric solidification shrinkage and volumetric solid contraction of 4% and 6% respectively. No riser is used. Assume uniform cooling in all directions. The side of the cube after solidification and contraction is[ME 2011]a)48.32 mmb)49.90 mmc)49.94 mmd)49.96 mmCorrect answer is option 'A'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A cubic casting of 50 mm side under goes volumetric solidification shrinkage and volumetric solid contraction of 4% and 6% respectively. No riser is used. Assume uniform cooling in all directions. The side of the cube after solidification and contraction is[ME 2011]a)48.32 mmb)49.90 mmc)49.94 mmd)49.96 mmCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cubic casting of 50 mm side under goes volumetric solidification shrinkage and volumetric solid contraction of 4% and 6% respectively. No riser is used. Assume uniform cooling in all directions. The side of the cube after solidification and contraction is[ME 2011]a)48.32 mmb)49.90 mmc)49.94 mmd)49.96 mmCorrect answer is option 'A'. Can you explain this answer?.
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