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A cube and sphere made of same material cast under identical conditions solidify at the same time. The ratio of length of cube to diameter of sphere is __________
- a)1
- b)1
Correct answer is between ' 1, 1'. Can you explain this answer?
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Understanding the Problem
When a cube and a sphere made of the same material solidify at the same time, it implies that they have the same volume and surface area characteristics under identical conditions.
Volume of Cube and Sphere
- Cube Volume: V_cube = L^3, where L is the length of one side of the cube.
- Sphere Volume: V_sphere = (4/3)π(R^3), where R is the radius of the sphere.
To relate the two, we need to express the diameter of the sphere in terms of its radius:
- Diameter of Sphere: D = 2R.
Condition for Equal Solidification Time
The solidification time is influenced by the surface area to volume ratio. For identical solidification times, the surface area to volume ratio should be similar for both shapes.
Surface Area of Cube and Sphere
- Cube Surface Area: A_cube = 6L^2.
- Sphere Surface Area: A_sphere = 4πR^2.
Finding the Ratio
To find the ratio of the length of the cube (L) to the diameter of the sphere (D):
1. Set the volumes equal:
L^3 = (4/3)π(R^3).
2. The surface areas can be compared, but for this question, we focus on the ratio of dimensions.
The ratio can be simplified as:
- L / D = L / (2R).
Given the solidification condition, we find that the ratio falls between 1 and 1:
- This implies that L is proportional to D, and thus the ratio remains consistent.
Conclusion
Hence, the ratio of the length of the cube to the diameter of the sphere is effectively around 1, which indicates that both shapes maintain a similar relationship in dimensions when subjected to identical solidification conditions.
When a cube and a sphere made of the same material solidify at the same time, it implies that they have the same volume and surface area characteristics under identical conditions.
Volume of Cube and Sphere
- Cube Volume: V_cube = L^3, where L is the length of one side of the cube.
- Sphere Volume: V_sphere = (4/3)π(R^3), where R is the radius of the sphere.
To relate the two, we need to express the diameter of the sphere in terms of its radius:
- Diameter of Sphere: D = 2R.
Condition for Equal Solidification Time
The solidification time is influenced by the surface area to volume ratio. For identical solidification times, the surface area to volume ratio should be similar for both shapes.
Surface Area of Cube and Sphere
- Cube Surface Area: A_cube = 6L^2.
- Sphere Surface Area: A_sphere = 4πR^2.
Finding the Ratio
To find the ratio of the length of the cube (L) to the diameter of the sphere (D):
1. Set the volumes equal:
L^3 = (4/3)π(R^3).
2. The surface areas can be compared, but for this question, we focus on the ratio of dimensions.
The ratio can be simplified as:
- L / D = L / (2R).
Given the solidification condition, we find that the ratio falls between 1 and 1:
- This implies that L is proportional to D, and thus the ratio remains consistent.
Conclusion
Hence, the ratio of the length of the cube to the diameter of the sphere is effectively around 1, which indicates that both shapes maintain a similar relationship in dimensions when subjected to identical solidification conditions.
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A cube and sphere made of same material cast under identical conditions solidify at the same time. The ratio of length of cube to diameter of sphere is __________a) 1b) 1Correct answer is between ' 1, 1'. 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 cube and sphere made of same material cast under identical conditions solidify at the same time. The ratio of length of cube to diameter of sphere is __________a) 1b) 1Correct answer is between ' 1, 1'. 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 cube and sphere made of same material cast under identical conditions solidify at the same time. The ratio of length of cube to diameter of sphere is __________a) 1b) 1Correct answer is between ' 1, 1'. Can you explain this answer?.
A cube and sphere made of same material cast under identical conditions solidify at the same time. The ratio of length of cube to diameter of sphere is __________a) 1b) 1Correct answer is between ' 1, 1'. 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 cube and sphere made of same material cast under identical conditions solidify at the same time. The ratio of length of cube to diameter of sphere is __________a) 1b) 1Correct answer is between ' 1, 1'. 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 cube and sphere made of same material cast under identical conditions solidify at the same time. The ratio of length of cube to diameter of sphere is __________a) 1b) 1Correct answer is between ' 1, 1'. Can you explain this answer?.
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