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Water flows out through a circular pipe whose internal radius 1 cm at the rate of 8 cm3/sec into an empty cylindrical tank, the radius of whose base is 40 cm. By how much will the level of water rise in the tank in half an hour?
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Water flows out through a circular pipe whose internal radius 1 cm at ...
Understanding the Problem
To determine how much the water level will rise in the cylindrical tank, we need to calculate the volume of water entering the tank over a specified time and then relate that to the change in height of the water in the tank.
Flow Rate of Water
- Water flows out of the pipe at a rate of 8 cm³/sec.
- In half an hour (30 minutes), the total volume of water can be calculated as follows:
- Total time in seconds: 30 minutes x 60 seconds/minute = 1800 seconds.
- Total volume = Flow rate x Time = 8 cm³/sec x 1800 sec = 14400 cm³.
Volume of the Cylindrical Tank
- The radius of the base of the cylindrical tank is 40 cm.
- The formula for the volume of a cylinder is:
Volume = π × r² × h
- We need to find the height increase (h) in the tank when the volume is 14400 cm³.
Calculating the Height Increase
1. Area of the base of the tank:
- Area = π × (40 cm)² = 1600π cm².
2. Setting up the equation:
- 14400 cm³ = 1600π cm² × h.
3. Solving for h:
- h = 14400 cm³ / (1600π cm²)
- h ≈ 2.865 cm (using π ≈ 3.14).
Conclusion
After half an hour, the level of water in the tank will rise approximately 2.87 cm. This calculation shows the relationship between the volume of water flowing in and the resultant increase in water level in the cylindrical tank.
To determine how much the water level will rise in the cylindrical tank, we need to calculate the volume of water entering the tank over a specified time and then relate that to the change in height of the water in the tank.
Flow Rate of Water
- Water flows out of the pipe at a rate of 8 cm³/sec.
- In half an hour (30 minutes), the total volume of water can be calculated as follows:
- Total time in seconds: 30 minutes x 60 seconds/minute = 1800 seconds.
- Total volume = Flow rate x Time = 8 cm³/sec x 1800 sec = 14400 cm³.
Volume of the Cylindrical Tank
- The radius of the base of the cylindrical tank is 40 cm.
- The formula for the volume of a cylinder is:
Volume = π × r² × h
- We need to find the height increase (h) in the tank when the volume is 14400 cm³.
Calculating the Height Increase
1. Area of the base of the tank:
- Area = π × (40 cm)² = 1600π cm².
2. Setting up the equation:
- 14400 cm³ = 1600π cm² × h.
3. Solving for h:
- h = 14400 cm³ / (1600π cm²)
- h ≈ 2.865 cm (using π ≈ 3.14).
Conclusion
After half an hour, the level of water in the tank will rise approximately 2.87 cm. This calculation shows the relationship between the volume of water flowing in and the resultant increase in water level in the cylindrical tank.
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Water flows out through a circular pipe whose internal radius 1 cm at ...
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Water flows out through a circular pipe whose internal radius 1 cm at the rate of 8 cm3/sec into an empty cylindrical tank, the radius of whose base is 40 cm. By how much will the level of water rise in the tank in half an hour? 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 out through a circular pipe whose internal radius 1 cm at the rate of 8 cm3/sec into an empty cylindrical tank, the radius of whose base is 40 cm. By how much will the level of water rise in the tank in half an hour? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Water flows out through a circular pipe whose internal radius 1 cm at the rate of 8 cm3/sec into an empty cylindrical tank, the radius of whose base is 40 cm. By how much will the level of water rise in the tank in half an hour?.
Water flows out through a circular pipe whose internal radius 1 cm at the rate of 8 cm3/sec into an empty cylindrical tank, the radius of whose base is 40 cm. By how much will the level of water rise in the tank in half an hour? 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 out through a circular pipe whose internal radius 1 cm at the rate of 8 cm3/sec into an empty cylindrical tank, the radius of whose base is 40 cm. By how much will the level of water rise in the tank in half an hour? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Water flows out through a circular pipe whose internal radius 1 cm at the rate of 8 cm3/sec into an empty cylindrical tank, the radius of whose base is 40 cm. By how much will the level of water rise in the tank in half an hour?.
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