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A tank holds 100 gallons of water. Its inlet is 7 inches in diameter and fills the tank at 5gallons/min. The outlet of the tank is twice the diameter of the inlet. How many minutes will ittake to empty the tank if the inlet is shut off, when the tank is full and the outlet is opened? (Hint: Rate of filling or emptying is directly proportional to the diameter)
- a)7.14 min
- b)10.0 min
- c)0.7 min
- d)5.0 min
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A tank holds 100 gallons of water. Its inlet is 7 inches in diameter a...
The outlet pipe will empty the tank at a rate which is double the rate of filling (Hence, 10 gallons
per minute). If the inlet is shut off, the tank will get emptied of 100 gallons of water in ten minutes.
per minute). If the inlet is shut off, the tank will get emptied of 100 gallons of water in ten minutes.
Most Upvoted Answer
A tank holds 100 gallons of water. Its inlet is 7 inches in diameter a...
Given data:
- Capacity of tank = 100 gallons
- Inlet diameter = 7 inches
- Inlet rate = 5 gallons/min
- Outlet diameter = 2 * Inlet diameter = 14 inches
To find: Time taken to empty the tank when the inlet is shut off and outlet is opened.
Approach:
- We know that the rate of filling or emptying is directly proportional to the diameter.
- Let's assume that the tank is cylindrical in shape and its height is h.
- We can use the formula for the volume of a cylinder to find the height of the tank.
Formula for the volume of a cylinder:
Volume = π * r^2 * h
where π = 3.14, r = radius of the cylinder, and h = height of the cylinder.
Let's find the height of the tank:
Capacity of tank = Volume of water in the tank
100 gallons = π * (7/2)^2 * h
100 = 3.14 * 24.5 * h
h = 100 / (3.14 * 24.5)
h = 1.29 feet
Now, let's find the rate of outlet:
As the outlet diameter is twice the inlet diameter, the outlet area is four times the inlet area.
Let's assume the velocity of water is the same at both the inlet and outlet.
So, the rate of outlet = 4 * rate of inlet
Rate of outlet = 4 * 5 = 20 gallons/min
Time taken to empty the tank:
Let's assume that the tank is full and the inlet is shut off.
The rate of emptying is 20 gallons/min.
So, time taken to empty the tank = Capacity of tank / Rate of emptying
= 100 gallons / 20 gallons/min
= 5 min
Therefore, the time taken to empty the tank when the inlet is shut off and outlet is opened is 5 minutes.
- Capacity of tank = 100 gallons
- Inlet diameter = 7 inches
- Inlet rate = 5 gallons/min
- Outlet diameter = 2 * Inlet diameter = 14 inches
To find: Time taken to empty the tank when the inlet is shut off and outlet is opened.
Approach:
- We know that the rate of filling or emptying is directly proportional to the diameter.
- Let's assume that the tank is cylindrical in shape and its height is h.
- We can use the formula for the volume of a cylinder to find the height of the tank.
Formula for the volume of a cylinder:
Volume = π * r^2 * h
where π = 3.14, r = radius of the cylinder, and h = height of the cylinder.
Let's find the height of the tank:
Capacity of tank = Volume of water in the tank
100 gallons = π * (7/2)^2 * h
100 = 3.14 * 24.5 * h
h = 100 / (3.14 * 24.5)
h = 1.29 feet
Now, let's find the rate of outlet:
As the outlet diameter is twice the inlet diameter, the outlet area is four times the inlet area.
Let's assume the velocity of water is the same at both the inlet and outlet.
So, the rate of outlet = 4 * rate of inlet
Rate of outlet = 4 * 5 = 20 gallons/min
Time taken to empty the tank:
Let's assume that the tank is full and the inlet is shut off.
The rate of emptying is 20 gallons/min.
So, time taken to empty the tank = Capacity of tank / Rate of emptying
= 100 gallons / 20 gallons/min
= 5 min
Therefore, the time taken to empty the tank when the inlet is shut off and outlet is opened is 5 minutes.
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A tank holds 100 gallons of water. Its inlet is 7 inches in diameter and fills the tank at 5gallons/min. The outlet of the tank is twice the diameter of the inlet. How many minutes will ittake to empty the tank if the inlet is shut off, when the tank is full and the outlet is opened? (Hint: Rate of filling or emptying is directly proportional to the diameter)a)7.14 minb)10.0 minc)0.7 mind)5.0 minCorrect answer is option 'B'. Can you explain this answer?
Question Description
A tank holds 100 gallons of water. Its inlet is 7 inches in diameter and fills the tank at 5gallons/min. The outlet of the tank is twice the diameter of the inlet. How many minutes will ittake to empty the tank if the inlet is shut off, when the tank is full and the outlet is opened? (Hint: Rate of filling or emptying is directly proportional to the diameter)a)7.14 minb)10.0 minc)0.7 mind)5.0 minCorrect answer is option 'B'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A tank holds 100 gallons of water. Its inlet is 7 inches in diameter and fills the tank at 5gallons/min. The outlet of the tank is twice the diameter of the inlet. How many minutes will ittake to empty the tank if the inlet is shut off, when the tank is full and the outlet is opened? (Hint: Rate of filling or emptying is directly proportional to the diameter)a)7.14 minb)10.0 minc)0.7 mind)5.0 minCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A tank holds 100 gallons of water. Its inlet is 7 inches in diameter and fills the tank at 5gallons/min. The outlet of the tank is twice the diameter of the inlet. How many minutes will ittake to empty the tank if the inlet is shut off, when the tank is full and the outlet is opened? (Hint: Rate of filling or emptying is directly proportional to the diameter)a)7.14 minb)10.0 minc)0.7 mind)5.0 minCorrect answer is option 'B'. Can you explain this answer?.
A tank holds 100 gallons of water. Its inlet is 7 inches in diameter and fills the tank at 5gallons/min. The outlet of the tank is twice the diameter of the inlet. How many minutes will ittake to empty the tank if the inlet is shut off, when the tank is full and the outlet is opened? (Hint: Rate of filling or emptying is directly proportional to the diameter)a)7.14 minb)10.0 minc)0.7 mind)5.0 minCorrect answer is option 'B'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A tank holds 100 gallons of water. Its inlet is 7 inches in diameter and fills the tank at 5gallons/min. The outlet of the tank is twice the diameter of the inlet. How many minutes will ittake to empty the tank if the inlet is shut off, when the tank is full and the outlet is opened? (Hint: Rate of filling or emptying is directly proportional to the diameter)a)7.14 minb)10.0 minc)0.7 mind)5.0 minCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A tank holds 100 gallons of water. Its inlet is 7 inches in diameter and fills the tank at 5gallons/min. The outlet of the tank is twice the diameter of the inlet. How many minutes will ittake to empty the tank if the inlet is shut off, when the tank is full and the outlet is opened? (Hint: Rate of filling or emptying is directly proportional to the diameter)a)7.14 minb)10.0 minc)0.7 mind)5.0 minCorrect answer is option 'B'. Can you explain this answer?.
Solutions for A tank holds 100 gallons of water. Its inlet is 7 inches in diameter and fills the tank at 5gallons/min. The outlet of the tank is twice the diameter of the inlet. How many minutes will ittake to empty the tank if the inlet is shut off, when the tank is full and the outlet is opened? (Hint: Rate of filling or emptying is directly proportional to the diameter)a)7.14 minb)10.0 minc)0.7 mind)5.0 minCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Quant.
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A tank holds 100 gallons of water. Its inlet is 7 inches in diameter and fills the tank at 5gallons/min. The outlet of the tank is twice the diameter of the inlet. How many minutes will ittake to empty the tank if the inlet is shut off, when the tank is full and the outlet is opened? (Hint: Rate of filling or emptying is directly proportional to the diameter)a)7.14 minb)10.0 minc)0.7 mind)5.0 minCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for A tank holds 100 gallons of water. Its inlet is 7 inches in diameter and fills the tank at 5gallons/min. The outlet of the tank is twice the diameter of the inlet. How many minutes will ittake to empty the tank if the inlet is shut off, when the tank is full and the outlet is opened? (Hint: Rate of filling or emptying is directly proportional to the diameter)a)7.14 minb)10.0 minc)0.7 mind)5.0 minCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of A tank holds 100 gallons of water. Its inlet is 7 inches in diameter and fills the tank at 5gallons/min. The outlet of the tank is twice the diameter of the inlet. How many minutes will ittake to empty the tank if the inlet is shut off, when the tank is full and the outlet is opened? (Hint: Rate of filling or emptying is directly proportional to the diameter)a)7.14 minb)10.0 minc)0.7 mind)5.0 minCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A tank holds 100 gallons of water. Its inlet is 7 inches in diameter and fills the tank at 5gallons/min. The outlet of the tank is twice the diameter of the inlet. How many minutes will ittake to empty the tank if the inlet is shut off, when the tank is full and the outlet is opened? (Hint: Rate of filling or emptying is directly proportional to the diameter)a)7.14 minb)10.0 minc)0.7 mind)5.0 minCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice Quant tests.
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