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For casting Aluminium cube of sides 15cm.The volume of shrinkage of aluminium during solidification is 6.5%.If cylindrical top riser is used then what will be height of cylinder?
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For casting Aluminium cube of sides 15cm.The volume of shrinkage of al...
Solution:
Given data:
Side of the cube = 15 cm
Volume of shrinkage = 6.5%
To find: Height of cylindrical top riser
Calculation:
Volume of the cube = (Side)^3
Volume of the cube = (15 cm)^3 = 3375 cm^3
Volume of the shrinkage = (6.5/100) x 3375 cm^3 = 219.4 cm^3
Total volume of the cube + shrinkage = 3375 + 219.4 = 3594.4 cm^3
Volume of cylindrical top riser = Volume of shrinkage
Volume of cylindrical top riser = 219.4 cm^3
Volume of cylindrical top riser = πr^2h
Radius of the cylindrical top riser = Side of the cube/2
Radius of the cylindrical top riser = 15/2 = 7.5 cm
Height of the cylindrical top riser = Volume of cylindrical top riser/πr^2
Height of the cylindrical top riser = 219.4/π(7.5)^2 = 1.23 cm
Therefore, the height of the cylindrical top riser is 1.23 cm.
Explanation:
Shrinkage occurs during the solidification process of molten metal due to the contraction of the metal as it cools down. To compensate for the shrinkage, a riser is used. In this case, a cylindrical top riser is used.
The volume of the cube is calculated using the given side length. The volume of shrinkage is calculated using the given percentage of shrinkage. The total volume of the cube and shrinkage is calculated by adding the volume of the cube and shrinkage.
The volume of the cylindrical top riser is equal to the volume of shrinkage. The radius of the cylindrical top riser is equal to half of the side length of the cube. The height of the cylindrical top riser is calculated using the formula for the volume of a cylinder.
The height of the cylindrical top riser is 1.23 cm, which is the required answer.
Given data:
Side of the cube = 15 cm
Volume of shrinkage = 6.5%
To find: Height of cylindrical top riser
Calculation:
Volume of the cube = (Side)^3
Volume of the cube = (15 cm)^3 = 3375 cm^3
Volume of the shrinkage = (6.5/100) x 3375 cm^3 = 219.4 cm^3
Total volume of the cube + shrinkage = 3375 + 219.4 = 3594.4 cm^3
Volume of cylindrical top riser = Volume of shrinkage
Volume of cylindrical top riser = 219.4 cm^3
Volume of cylindrical top riser = πr^2h
Radius of the cylindrical top riser = Side of the cube/2
Radius of the cylindrical top riser = 15/2 = 7.5 cm
Height of the cylindrical top riser = Volume of cylindrical top riser/πr^2
Height of the cylindrical top riser = 219.4/π(7.5)^2 = 1.23 cm
Therefore, the height of the cylindrical top riser is 1.23 cm.
Explanation:
Shrinkage occurs during the solidification process of molten metal due to the contraction of the metal as it cools down. To compensate for the shrinkage, a riser is used. In this case, a cylindrical top riser is used.
The volume of the cube is calculated using the given side length. The volume of shrinkage is calculated using the given percentage of shrinkage. The total volume of the cube and shrinkage is calculated by adding the volume of the cube and shrinkage.
The volume of the cylindrical top riser is equal to the volume of shrinkage. The radius of the cylindrical top riser is equal to half of the side length of the cube. The height of the cylindrical top riser is calculated using the formula for the volume of a cylinder.
The height of the cylindrical top riser is 1.23 cm, which is the required answer.
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For casting Aluminium cube of sides 15cm.The volume of shrinkage of aluminium during solidification is 6.5%.If cylindrical top riser is used then what will be height of cylinder?
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For casting Aluminium cube of sides 15cm.The volume of shrinkage of aluminium during solidification is 6.5%.If cylindrical top riser is used then what will be height of cylinder? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about For casting Aluminium cube of sides 15cm.The volume of shrinkage of aluminium during solidification is 6.5%.If cylindrical top riser is used then what will be height of cylinder? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For casting Aluminium cube of sides 15cm.The volume of shrinkage of aluminium during solidification is 6.5%.If cylindrical top riser is used then what will be height of cylinder?.
For casting Aluminium cube of sides 15cm.The volume of shrinkage of aluminium during solidification is 6.5%.If cylindrical top riser is used then what will be height of cylinder? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about For casting Aluminium cube of sides 15cm.The volume of shrinkage of aluminium during solidification is 6.5%.If cylindrical top riser is used then what will be height of cylinder? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For casting Aluminium cube of sides 15cm.The volume of shrinkage of aluminium during solidification is 6.5%.If cylindrical top riser is used then what will be height of cylinder?.
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