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A cylindrical tank of diameter 7 M and height 10 M is connected with a cylindrical pipe of area of cross section 154 cm square if the water flow in the pipe is 6 km per hour find how much time will it take to fill the tank completely?
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A cylindrical tank of diameter 7 M and height 10 M is connected with a...
Problem Analysis:
We are given a cylindrical tank with diameter 7 M and height 10 M. The tank is connected to a cylindrical pipe with an area of cross section of 154 cm square. We need to find the time it will take to fill the tank completely.
Conversion:
Before we proceed, let's convert the given values to a consistent unit.
1 M = 100 cm
Diameter = 7 M = 7 * 100 cm = 700 cm
Height = 10 M = 10 * 100 cm = 1000 cm
Area of cross section = 154 cm square
Calculation:
To find the time it takes to fill the tank completely, we need to calculate the volume of the tank and the rate of water flow.
Volume of the tank:
The volume of a cylinder is given by the formula:
Volume = π * (radius)^2 * height
Since we are given the diameter, we can calculate the radius as half of the diameter:
Radius = diameter / 2 = 700 cm / 2 = 350 cm
Substituting the values into the formula:
Volume = π * (350 cm)^2 * 1000 cm = 3.85 * 10^8 cm^3
Rate of water flow:
The rate of water flow is given in km per hour. We need to convert it to cm^3 per hour.
1 km = 100000 cm
1 hour = 60 minutes
1 minute = 60 seconds
So, the rate of water flow in cm^3 per hour is:
Rate of flow = 6 km/hour * 100000 cm/km = 6 * 10^5 cm/hour
Time to fill the tank:
To find the time it takes to fill the tank completely, we can divide the volume of the tank by the rate of water flow.
Time = Volume / Rate of flow
Time = (3.85 * 10^8 cm^3) / (6 * 10^5 cm/hour)
Simplifying the expression:
Time = 641.67 hours
Answer:
It will take approximately 641.67 hours to fill the tank completely.
We are given a cylindrical tank with diameter 7 M and height 10 M. The tank is connected to a cylindrical pipe with an area of cross section of 154 cm square. We need to find the time it will take to fill the tank completely.
Conversion:
Before we proceed, let's convert the given values to a consistent unit.
1 M = 100 cm
Diameter = 7 M = 7 * 100 cm = 700 cm
Height = 10 M = 10 * 100 cm = 1000 cm
Area of cross section = 154 cm square
Calculation:
To find the time it takes to fill the tank completely, we need to calculate the volume of the tank and the rate of water flow.
Volume of the tank:
The volume of a cylinder is given by the formula:
Volume = π * (radius)^2 * height
Since we are given the diameter, we can calculate the radius as half of the diameter:
Radius = diameter / 2 = 700 cm / 2 = 350 cm
Substituting the values into the formula:
Volume = π * (350 cm)^2 * 1000 cm = 3.85 * 10^8 cm^3
Rate of water flow:
The rate of water flow is given in km per hour. We need to convert it to cm^3 per hour.
1 km = 100000 cm
1 hour = 60 minutes
1 minute = 60 seconds
So, the rate of water flow in cm^3 per hour is:
Rate of flow = 6 km/hour * 100000 cm/km = 6 * 10^5 cm/hour
Time to fill the tank:
To find the time it takes to fill the tank completely, we can divide the volume of the tank by the rate of water flow.
Time = Volume / Rate of flow
Time = (3.85 * 10^8 cm^3) / (6 * 10^5 cm/hour)
Simplifying the expression:
Time = 641.67 hours
Answer:
It will take approximately 641.67 hours to fill the tank completely.
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A cylindrical tank of diameter 7 M and height 10 M is connected with a cylindrical pipe of area of cross section 154 cm square if the water flow in the pipe is 6 km per hour find how much time will it take to fill the tank completely?
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A cylindrical tank of diameter 7 M and height 10 M is connected with a cylindrical pipe of area of cross section 154 cm square if the water flow in the pipe is 6 km per hour find how much time will it take to fill the tank completely? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about A cylindrical tank of diameter 7 M and height 10 M is connected with a cylindrical pipe of area of cross section 154 cm square if the water flow in the pipe is 6 km per hour find how much time will it take to fill the tank completely? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cylindrical tank of diameter 7 M and height 10 M is connected with a cylindrical pipe of area of cross section 154 cm square if the water flow in the pipe is 6 km per hour find how much time will it take to fill the tank completely?.
A cylindrical tank of diameter 7 M and height 10 M is connected with a cylindrical pipe of area of cross section 154 cm square if the water flow in the pipe is 6 km per hour find how much time will it take to fill the tank completely? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about A cylindrical tank of diameter 7 M and height 10 M is connected with a cylindrical pipe of area of cross section 154 cm square if the water flow in the pipe is 6 km per hour find how much time will it take to fill the tank completely? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cylindrical tank of diameter 7 M and height 10 M is connected with a cylindrical pipe of area of cross section 154 cm square if the water flow in the pipe is 6 km per hour find how much time will it take to fill the tank completely?.
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