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Water flows in a tank 150 m × 100 m at the base through a pipe whose cross-section is 2 dm by 1.5 dm at the speed of 15 km per hour. At what time will the water be 3 meters deep?
- a)100 hours
- b)120 hours
- c)80 hours
- d)150 hours
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Water flows in a tank 150 m × 100 m at the base through a pipe w...
Understanding the Problem
To determine how long it will take for the water in the tank to reach a depth of 3 meters, we need to calculate the volume of water required and the volume flow rate through the pipe.
Tank and Water Volume
- The dimensions of the tank are 150 m × 100 m.
- The required depth of water is 3 m.
Calculating the Volume of Water Needed
- Volume of water (V) = length × width × height
- V = 150 m × 100 m × 3 m = 45,000 cubic meters.
Pipe Cross-Section and Flow Speed
- The cross-section of the pipe is 2 dm × 1.5 dm, which converts to meters as:
- 2 dm = 0.2 m
- 1.5 dm = 0.15 m
- Cross-sectional area (A) = 0.2 m × 0.15 m = 0.03 square meters.
Flow Rate Calculation
- Speed of water flow = 15 km/h = 15,000 m/3600 s = 4.167 m/s.
- Flow rate (Q) = Area × Speed = 0.03 m² × 4.167 m/s = 0.125 m³/s.
Time Required to Fill the Tank
- To find the time (t) to fill 45,000 m³, we use the formula:
- t = Volume / Flow Rate = 45,000 m³ / 0.125 m³/s = 360,000 seconds.
Convert Time to Hours
- Convert seconds to hours:
- 360,000 seconds ÷ 3600 seconds/hour = 100 hours.
Conclusion
The time required for the water to reach a depth of 3 meters in the tank is 100 hours, making option 'A' the correct answer.
To determine how long it will take for the water in the tank to reach a depth of 3 meters, we need to calculate the volume of water required and the volume flow rate through the pipe.
Tank and Water Volume
- The dimensions of the tank are 150 m × 100 m.
- The required depth of water is 3 m.
Calculating the Volume of Water Needed
- Volume of water (V) = length × width × height
- V = 150 m × 100 m × 3 m = 45,000 cubic meters.
Pipe Cross-Section and Flow Speed
- The cross-section of the pipe is 2 dm × 1.5 dm, which converts to meters as:
- 2 dm = 0.2 m
- 1.5 dm = 0.15 m
- Cross-sectional area (A) = 0.2 m × 0.15 m = 0.03 square meters.
Flow Rate Calculation
- Speed of water flow = 15 km/h = 15,000 m/3600 s = 4.167 m/s.
- Flow rate (Q) = Area × Speed = 0.03 m² × 4.167 m/s = 0.125 m³/s.
Time Required to Fill the Tank
- To find the time (t) to fill 45,000 m³, we use the formula:
- t = Volume / Flow Rate = 45,000 m³ / 0.125 m³/s = 360,000 seconds.
Convert Time to Hours
- Convert seconds to hours:
- 360,000 seconds ÷ 3600 seconds/hour = 100 hours.
Conclusion
The time required for the water to reach a depth of 3 meters in the tank is 100 hours, making option 'A' the correct answer.
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Community Answer
Water flows in a tank 150 m × 100 m at the base through a pipe w...
The volume of water in the tank
= 150 × 100 × 3 = 45000 m3
Area of a cross-section of the pipe
= 2dm × 1.5dm
Let the time taken be t hours.
The volume of water that flows in a tank in t hours.
= 450 t m3
⇒ 450t = 45000
⇒ t = 45000/450 = 100 hours
= 150 × 100 × 3 = 45000 m3
Area of a cross-section of the pipe
= 2dm × 1.5dm
Let the time taken be t hours.
The volume of water that flows in a tank in t hours.
= 450 t m3
⇒ 450t = 45000
⇒ t = 45000/450 = 100 hours
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Water flows in a tank 150 m × 100 m at the base through a pipe whose cross-section is 2 dm by 1.5 dm at the speed of 15 km per hour. At what time will the water be 3 meters deep?a)100 hoursb)120 hoursc)80 hoursd)150 hoursCorrect answer is option 'A'. Can you explain this answer? for Class 9 2025 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Water flows in a tank 150 m × 100 m at the base through a pipe whose cross-section is 2 dm by 1.5 dm at the speed of 15 km per hour. At what time will the water be 3 meters deep?a)100 hoursb)120 hoursc)80 hoursd)150 hoursCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Water flows in a tank 150 m × 100 m at the base through a pipe whose cross-section is 2 dm by 1.5 dm at the speed of 15 km per hour. At what time will the water be 3 meters deep?a)100 hoursb)120 hoursc)80 hoursd)150 hoursCorrect answer is option 'A'. Can you explain this answer?.
Water flows in a tank 150 m × 100 m at the base through a pipe whose cross-section is 2 dm by 1.5 dm at the speed of 15 km per hour. At what time will the water be 3 meters deep?a)100 hoursb)120 hoursc)80 hoursd)150 hoursCorrect answer is option 'A'. Can you explain this answer? for Class 9 2025 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Water flows in a tank 150 m × 100 m at the base through a pipe whose cross-section is 2 dm by 1.5 dm at the speed of 15 km per hour. At what time will the water be 3 meters deep?a)100 hoursb)120 hoursc)80 hoursd)150 hoursCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Water flows in a tank 150 m × 100 m at the base through a pipe whose cross-section is 2 dm by 1.5 dm at the speed of 15 km per hour. At what time will the water be 3 meters deep?a)100 hoursb)120 hoursc)80 hoursd)150 hoursCorrect answer is option 'A'. Can you explain this answer?.
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Water flows in a tank 150 m × 100 m at the base through a pipe whose cross-section is 2 dm by 1.5 dm at the speed of 15 km per hour. At what time will the water be 3 meters deep?a)100 hoursb)120 hoursc)80 hoursd)150 hoursCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for Water flows in a tank 150 m × 100 m at the base through a pipe whose cross-section is 2 dm by 1.5 dm at the speed of 15 km per hour. At what time will the water be 3 meters deep?a)100 hoursb)120 hoursc)80 hoursd)150 hoursCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of Water flows in a tank 150 m × 100 m at the base through a pipe whose cross-section is 2 dm by 1.5 dm at the speed of 15 km per hour. At what time will the water be 3 meters deep?a)100 hoursb)120 hoursc)80 hoursd)150 hoursCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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