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A cylindrical job with diameter of 200 mm and height of 100 mm is to be cast using modulus method of riser design. Assume that the bottom surface of cylindrical riser does not contribute as cooling surface. If the diameter of the riser is equal to its height, then the height of the riser (in mm) is
- a)150
- b)200
- c)100
- d)125
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A cylindrical job with diameter of 200 mm and height of 100 mm is to b...
To determine the height of the riser using the modulus method of riser design, we need to consider the cooling surface area of the riser and the casting.
Given:
Diameter of the cylindrical job = 200 mm
Height of the cylindrical job = 100 mm
Step 1: Calculate the cooling surface area of the cylindrical job
The cooling surface area can be calculated using the formula:
Cooling Surface Area = π × Diameter × Height
Given:
Diameter of the cylindrical job = 200 mm
Height of the cylindrical job = 100 mm
Cooling Surface Area = π × 200 mm × 100 mm
Cooling Surface Area = 62,800 mm²
Step 2: Calculate the required volume of the riser
The volume of the riser can be calculated using the formula:
Volume = π/4 × Diameter² × Height
Given:
Diameter of the riser = Height of the riser (since the diameter of the riser is equal to its height)
Volume = π/4 × (Height)² × Height
Volume = π/4 × Height³
Step 3: Calculate the required cooling surface area of the riser
The required cooling surface area of the riser is equal to the cooling surface area of the cylindrical job.
Required Cooling Surface Area of the Riser = Cooling Surface Area of the Cylindrical Job
62,800 mm² = π × (Height)² × Height
Step 4: Solve for the height of the riser
Divide both sides of the equation by π and solve for Height:
(Height)³ = 62,800 mm² / π
(Height)³ ≈ 20,000
Taking the cube root of both sides, we get:
Height ≈ ∛20,000 ≈ 27.14 mm
Since the height of the riser should be in whole numbers, we round up to the nearest whole number:
Height ≈ 28 mm
Therefore, the height of the riser is approximately 28 mm, which is not among the given answer options. It seems that there might be a mistake in either the question or the provided answer options.
Given:
Diameter of the cylindrical job = 200 mm
Height of the cylindrical job = 100 mm
Step 1: Calculate the cooling surface area of the cylindrical job
The cooling surface area can be calculated using the formula:
Cooling Surface Area = π × Diameter × Height
Given:
Diameter of the cylindrical job = 200 mm
Height of the cylindrical job = 100 mm
Cooling Surface Area = π × 200 mm × 100 mm
Cooling Surface Area = 62,800 mm²
Step 2: Calculate the required volume of the riser
The volume of the riser can be calculated using the formula:
Volume = π/4 × Diameter² × Height
Given:
Diameter of the riser = Height of the riser (since the diameter of the riser is equal to its height)
Volume = π/4 × (Height)² × Height
Volume = π/4 × Height³
Step 3: Calculate the required cooling surface area of the riser
The required cooling surface area of the riser is equal to the cooling surface area of the cylindrical job.
Required Cooling Surface Area of the Riser = Cooling Surface Area of the Cylindrical Job
62,800 mm² = π × (Height)² × Height
Step 4: Solve for the height of the riser
Divide both sides of the equation by π and solve for Height:
(Height)³ = 62,800 mm² / π
(Height)³ ≈ 20,000
Taking the cube root of both sides, we get:
Height ≈ ∛20,000 ≈ 27.14 mm
Since the height of the riser should be in whole numbers, we round up to the nearest whole number:
Height ≈ 28 mm
Therefore, the height of the riser is approximately 28 mm, which is not among the given answer options. It seems that there might be a mistake in either the question or the provided answer options.
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A cylindrical job with diameter of 200 mm and height of 100 mm is to be cast using modulus method of riser design. Assume that the bottom surface of cylindrical riser does not contribute as cooling surface. If the diameter of the riser is equal to its height, then the height of the riser (in mm) isa)150b)200c)100d)125Correct answer is option 'A'. Can you explain this answer?
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A cylindrical job with diameter of 200 mm and height of 100 mm is to be cast using modulus method of riser design. Assume that the bottom surface of cylindrical riser does not contribute as cooling surface. If the diameter of the riser is equal to its height, then the height of the riser (in mm) isa)150b)200c)100d)125Correct answer is option 'A'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A cylindrical job with diameter of 200 mm and height of 100 mm is to be cast using modulus method of riser design. Assume that the bottom surface of cylindrical riser does not contribute as cooling surface. If the diameter of the riser is equal to its height, then the height of the riser (in mm) isa)150b)200c)100d)125Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cylindrical job with diameter of 200 mm and height of 100 mm is to be cast using modulus method of riser design. Assume that the bottom surface of cylindrical riser does not contribute as cooling surface. If the diameter of the riser is equal to its height, then the height of the riser (in mm) isa)150b)200c)100d)125Correct answer is option 'A'. Can you explain this answer?.
A cylindrical job with diameter of 200 mm and height of 100 mm is to be cast using modulus method of riser design. Assume that the bottom surface of cylindrical riser does not contribute as cooling surface. If the diameter of the riser is equal to its height, then the height of the riser (in mm) isa)150b)200c)100d)125Correct answer is option 'A'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A cylindrical job with diameter of 200 mm and height of 100 mm is to be cast using modulus method of riser design. Assume that the bottom surface of cylindrical riser does not contribute as cooling surface. If the diameter of the riser is equal to its height, then the height of the riser (in mm) isa)150b)200c)100d)125Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cylindrical job with diameter of 200 mm and height of 100 mm is to be cast using modulus method of riser design. Assume that the bottom surface of cylindrical riser does not contribute as cooling surface. If the diameter of the riser is equal to its height, then the height of the riser (in mm) isa)150b)200c)100d)125Correct answer is option 'A'. Can you explain this answer?.
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