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A cube shaped casting solidifies in 5 minutes. The solidification time in minutes for a cube of the same material, which is 8 times heavier than the original casting will be
- a)10
- b)20
- c)24
- d)40
Correct answer is option 'B'. Can you explain this answer?
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A cube shaped casting solidifies in 5 minutes. The solidification time...
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A cube shaped casting solidifies in 5 minutes. The solidification time...
Problem Analysis:
- A cube shaped casting solidifies in 5 minutes.
- A cube of the same material, which is 8 times heavier than the original casting, is considered.
- We need to find the solidification time for this larger cube.
Solution:
Let's assume the solidification time for the larger cube is 't' minutes.
Relation between solidification time and volume:
- The solidification time is directly proportional to the volume of the casting.
- If the volume of a casting is 'V' and its solidification time is 't', then for a casting with 8 times the volume (i.e., 8V), the solidification time will be '8t'.
Relation between volume and weight:
- For a cube, the volume is directly proportional to the cube of its side length.
- If the side length of a cube is 'a' and its weight is 'W', then for a cube with 8 times the weight (i.e., 8W), the side length will become '2a' (since weight is proportional to the cube of the side length).
- Therefore, the volume of the larger cube will become (2a)^3 = 8a^3.
Relation between weight and solidification time:
- From the given information, we know that the weight of the larger cube is 8 times the weight of the original casting.
- Since the solidification time is directly proportional to the weight, the solidification time for the larger cube will also be 8 times the solidification time for the original casting.
Combining the above relations:
- We have the solidification time for the original casting as 5 minutes.
- The solidification time for the larger cube is 8 times the solidification time for the original casting.
- Therefore, the solidification time for the larger cube is 8 * 5 = 40 minutes.
Final Answer:
Therefore, the solidification time for a cube of the same material, which is 8 times heavier than the original casting, will be 40 minutes. (Option D)
- A cube shaped casting solidifies in 5 minutes.
- A cube of the same material, which is 8 times heavier than the original casting, is considered.
- We need to find the solidification time for this larger cube.
Solution:
Let's assume the solidification time for the larger cube is 't' minutes.
Relation between solidification time and volume:
- The solidification time is directly proportional to the volume of the casting.
- If the volume of a casting is 'V' and its solidification time is 't', then for a casting with 8 times the volume (i.e., 8V), the solidification time will be '8t'.
Relation between volume and weight:
- For a cube, the volume is directly proportional to the cube of its side length.
- If the side length of a cube is 'a' and its weight is 'W', then for a cube with 8 times the weight (i.e., 8W), the side length will become '2a' (since weight is proportional to the cube of the side length).
- Therefore, the volume of the larger cube will become (2a)^3 = 8a^3.
Relation between weight and solidification time:
- From the given information, we know that the weight of the larger cube is 8 times the weight of the original casting.
- Since the solidification time is directly proportional to the weight, the solidification time for the larger cube will also be 8 times the solidification time for the original casting.
Combining the above relations:
- We have the solidification time for the original casting as 5 minutes.
- The solidification time for the larger cube is 8 times the solidification time for the original casting.
- Therefore, the solidification time for the larger cube is 8 * 5 = 40 minutes.
Final Answer:
Therefore, the solidification time for a cube of the same material, which is 8 times heavier than the original casting, will be 40 minutes. (Option D)
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A cube shaped casting solidifies in 5 minutes. The solidification time in minutesfor a cube of the same material, which is 8 times heavier than the original castingwill bea)10b)20c)24d)40Correct answer is option 'B'. Can you explain this answer?
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