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Water flows at the rate of 10 m per minute from a cylindrical pipe 5 mm in diameter. A conical vessel whose diameter is 40 cm and depth 24 cm is filled. The time taken to fill the conical vessel is :
- a)50 min
- b)50 min. 12 sec.
- c)51 min. 12 sec
- d)51 min. 15 sec.
Correct answer is option 'C'. Can you explain this answer?
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To find the time taken to fill the conical vessel, we need to calculate the volume of water flowing per minute and then divide the volume of the vessel by the volume of water flowing per minute.
1. Calculate the cross-sectional area of the cylindrical pipe:
- The diameter of the pipe is 5 mm, which means the radius is 2.5 mm or 0.0025 m.
- The cross-sectional area of the pipe can be calculated using the formula: A = πr^2.
- Substituting the values, we get: A = π(0.0025)^2 = 0.00001963 m^2.
2. Calculate the volume of water flowing per minute:
- The water flows at a rate of 10 m per minute, so the length of water flowing per minute is 10 m.
- The volume of water flowing per minute can be calculated using the formula: V = A × l.
- Substituting the values, we get: V = 0.00001963 m^2 × 10 m = 0.0001963 m^3.
3. Calculate the volume of the conical vessel:
- The diameter of the vessel is 40 cm, which means the radius is 20 cm or 0.2 m.
- The depth of the vessel is 24 cm or 0.24 m.
- The volume of a cone can be calculated using the formula: V = (1/3)πr^2h.
- Substituting the values, we get: V = (1/3)π(0.2)^2 × 0.24 = 0.008π m^3.
4. Calculate the time taken to fill the conical vessel:
- Divide the volume of the vessel by the volume of water flowing per minute.
- (0.008π m^3) / (0.0001963 m^3/min) ≈ 40.6 min ≈ 41 min (rounded to the nearest minute).
Therefore, the time taken to fill the conical vessel is approximately 41 minutes. However, none of the given options match this answer.
1. Calculate the cross-sectional area of the cylindrical pipe:
- The diameter of the pipe is 5 mm, which means the radius is 2.5 mm or 0.0025 m.
- The cross-sectional area of the pipe can be calculated using the formula: A = πr^2.
- Substituting the values, we get: A = π(0.0025)^2 = 0.00001963 m^2.
2. Calculate the volume of water flowing per minute:
- The water flows at a rate of 10 m per minute, so the length of water flowing per minute is 10 m.
- The volume of water flowing per minute can be calculated using the formula: V = A × l.
- Substituting the values, we get: V = 0.00001963 m^2 × 10 m = 0.0001963 m^3.
3. Calculate the volume of the conical vessel:
- The diameter of the vessel is 40 cm, which means the radius is 20 cm or 0.2 m.
- The depth of the vessel is 24 cm or 0.24 m.
- The volume of a cone can be calculated using the formula: V = (1/3)πr^2h.
- Substituting the values, we get: V = (1/3)π(0.2)^2 × 0.24 = 0.008π m^3.
4. Calculate the time taken to fill the conical vessel:
- Divide the volume of the vessel by the volume of water flowing per minute.
- (0.008π m^3) / (0.0001963 m^3/min) ≈ 40.6 min ≈ 41 min (rounded to the nearest minute).
Therefore, the time taken to fill the conical vessel is approximately 41 minutes. However, none of the given options match this answer.
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Water flows at the rate of 10 m per minute from a cylindrical pipe 5 mm in diameter. A conical vessel whose diameter is 40 cm and depth 24 cm is filled. The time taken to fill the conical vessel is :a)50 minb)50 min. 12 sec.c)51 min. 12 secd)51 min. 15 sec.Correct answer is option 'C'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Water flows at the rate of 10 m per minute from a cylindrical pipe 5 mm in diameter. A conical vessel whose diameter is 40 cm and depth 24 cm is filled. The time taken to fill the conical vessel is :a)50 minb)50 min. 12 sec.c)51 min. 12 secd)51 min. 15 sec.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Water flows at the rate of 10 m per minute from a cylindrical pipe 5 mm in diameter. A conical vessel whose diameter is 40 cm and depth 24 cm is filled. The time taken to fill the conical vessel is :a)50 minb)50 min. 12 sec.c)51 min. 12 secd)51 min. 15 sec.Correct answer is option 'C'. Can you explain this answer?.
Water flows at the rate of 10 m per minute from a cylindrical pipe 5 mm in diameter. A conical vessel whose diameter is 40 cm and depth 24 cm is filled. The time taken to fill the conical vessel is :a)50 minb)50 min. 12 sec.c)51 min. 12 secd)51 min. 15 sec.Correct answer is option 'C'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Water flows at the rate of 10 m per minute from a cylindrical pipe 5 mm in diameter. A conical vessel whose diameter is 40 cm and depth 24 cm is filled. The time taken to fill the conical vessel is :a)50 minb)50 min. 12 sec.c)51 min. 12 secd)51 min. 15 sec.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Water flows at the rate of 10 m per minute from a cylindrical pipe 5 mm in diameter. A conical vessel whose diameter is 40 cm and depth 24 cm is filled. The time taken to fill the conical vessel is :a)50 minb)50 min. 12 sec.c)51 min. 12 secd)51 min. 15 sec.Correct answer is option 'C'. Can you explain this answer?.
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