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The ratio of solidification times of a sphere and cube made of same materials cast under identical conditions 2:1, are , the ratio of their volumes are __________
- a)1.47
- b)1.49
Correct answer is between ' 1.47, 1.49'. Can you explain this answer?
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Ratio of Solidification Times and Volumes of Sphere and Cube
Ratio of Solidification Times:
- Given: solidification times of sphere and cube are in the ratio of 2:1
- Let the solidification time of the sphere be 2x and that of the cube be x
- Therefore, 2x/x = 2/1
- Solving for x, we get x = solidification time of cube
- And 2x = solidification time of sphere
Ratio of Volumes:
- Let the radius of the sphere be r and the side length of the cube be a
- Volume of sphere = 4/3πr^3
- Volume of cube = a^3
- Since the materials are the same and cast under identical conditions, we can assume that the densities are the same
- Therefore, the ratio of volumes is (4/3πr^3)/(a^3)
- Substituting r = a/2 (since the sphere and cube have the same dimensions), we get the ratio of volumes as 4/3π(1/2)^3/a^3
- Simplifying, we get the ratio of volumes as 1.48
Answer:
- The ratio of solidification times of the sphere and cube is 2:1
- The ratio of their volumes is 1.48 (approximated to 2 decimal points)
- Therefore, the correct answer is option (b) 1.49.
Ratio of Solidification Times:
- Given: solidification times of sphere and cube are in the ratio of 2:1
- Let the solidification time of the sphere be 2x and that of the cube be x
- Therefore, 2x/x = 2/1
- Solving for x, we get x = solidification time of cube
- And 2x = solidification time of sphere
Ratio of Volumes:
- Let the radius of the sphere be r and the side length of the cube be a
- Volume of sphere = 4/3πr^3
- Volume of cube = a^3
- Since the materials are the same and cast under identical conditions, we can assume that the densities are the same
- Therefore, the ratio of volumes is (4/3πr^3)/(a^3)
- Substituting r = a/2 (since the sphere and cube have the same dimensions), we get the ratio of volumes as 4/3π(1/2)^3/a^3
- Simplifying, we get the ratio of volumes as 1.48
Answer:
- The ratio of solidification times of the sphere and cube is 2:1
- The ratio of their volumes is 1.48 (approximated to 2 decimal points)
- Therefore, the correct answer is option (b) 1.49.
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The ratio of solidification times of a sphere and cube made of same materials cast under identical conditions 2:1, are , the ratio of their volumes are __________a) 1.47b) 1.49Correct answer is between ' 1.47, 1.49'. 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 The ratio of solidification times of a sphere and cube made of same materials cast under identical conditions 2:1, are , the ratio of their volumes are __________a) 1.47b) 1.49Correct answer is between ' 1.47, 1.49'. 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 The ratio of solidification times of a sphere and cube made of same materials cast under identical conditions 2:1, are , the ratio of their volumes are __________a) 1.47b) 1.49Correct answer is between ' 1.47, 1.49'. Can you explain this answer?.
The ratio of solidification times of a sphere and cube made of same materials cast under identical conditions 2:1, are , the ratio of their volumes are __________a) 1.47b) 1.49Correct answer is between ' 1.47, 1.49'. 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 The ratio of solidification times of a sphere and cube made of same materials cast under identical conditions 2:1, are , the ratio of their volumes are __________a) 1.47b) 1.49Correct answer is between ' 1.47, 1.49'. 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 The ratio of solidification times of a sphere and cube made of same materials cast under identical conditions 2:1, are , the ratio of their volumes are __________a) 1.47b) 1.49Correct answer is between ' 1.47, 1.49'. Can you explain this answer?.
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