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Water flows at a rate of 10 m per minute from a cylindrical pipe, 5 mm in diameter. How long will it take to fill up a conical vessel whose diameter of the base is 40 cm and depth is 24 cm?
- a)48 min 15 sec
- b)51 min 12 sec
- c)52 min 1 sec
- d)55 min
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Water flows at a rate of 10 m per minute from a cylindrical pipe, 5 mm...
To find the time it takes to fill up a conical vessel, we need to first calculate the volume of the vessel and then divide it by the rate at which water flows from the pipe.
Volume of a cone:
The volume of a cone can be calculated using the formula: V = (1/3) * π * r^2 * h, where V is the volume, π is a constant approximately equal to 3.14, r is the radius of the base, and h is the height of the cone.
Given information:
- Diameter of the base of the conical vessel = 40 cm
- Radius of the base (r) = diameter/2 = 40/2 = 20 cm = 0.2 m
- Depth of the conical vessel (h) = 24 cm = 0.24 m
Calculating the volume of the conical vessel:
V = (1/3) * π * 0.2^2 * 0.24
V ≈ 0.01 m^3
Flow rate of water:
Water flows at a rate of 10 m per minute from the pipe.
Calculating the time taken to fill the vessel:
Time = Volume / Flow rate
Time = 0.01 m^3 / 10 m/min
Time = 0.001 min
Converting minutes to minutes and seconds:
0.001 min * 60 sec/min = 0.06 sec
Therefore, it will take approximately 0.06 seconds to fill up the conical vessel.
Converting seconds to minutes and seconds:
0.06 sec ≈ 0 min 4.8 sec
Therefore, it will take approximately 0 minutes and 4.8 seconds to fill up the conical vessel.
Rounding off to the nearest second:
0 min 4.8 sec ≈ 0 min 5 sec
Therefore, it will take approximately 0 minutes and 5 seconds to fill up the conical vessel.
Converting minutes to minutes and seconds:
0 min 5 sec ≈ 0 min 0 sec
Therefore, it will take approximately 0 minutes and 0 seconds to fill up the conical vessel.
Adding the time taken in minutes:
0 min + 0 min = 0 min
Therefore, it will take approximately 0 minutes to fill up the conical vessel.
However, none of the given options match the calculated time. Please check the question and options again.
Volume of a cone:
The volume of a cone can be calculated using the formula: V = (1/3) * π * r^2 * h, where V is the volume, π is a constant approximately equal to 3.14, r is the radius of the base, and h is the height of the cone.
Given information:
- Diameter of the base of the conical vessel = 40 cm
- Radius of the base (r) = diameter/2 = 40/2 = 20 cm = 0.2 m
- Depth of the conical vessel (h) = 24 cm = 0.24 m
Calculating the volume of the conical vessel:
V = (1/3) * π * 0.2^2 * 0.24
V ≈ 0.01 m^3
Flow rate of water:
Water flows at a rate of 10 m per minute from the pipe.
Calculating the time taken to fill the vessel:
Time = Volume / Flow rate
Time = 0.01 m^3 / 10 m/min
Time = 0.001 min
Converting minutes to minutes and seconds:
0.001 min * 60 sec/min = 0.06 sec
Therefore, it will take approximately 0.06 seconds to fill up the conical vessel.
Converting seconds to minutes and seconds:
0.06 sec ≈ 0 min 4.8 sec
Therefore, it will take approximately 0 minutes and 4.8 seconds to fill up the conical vessel.
Rounding off to the nearest second:
0 min 4.8 sec ≈ 0 min 5 sec
Therefore, it will take approximately 0 minutes and 5 seconds to fill up the conical vessel.
Converting minutes to minutes and seconds:
0 min 5 sec ≈ 0 min 0 sec
Therefore, it will take approximately 0 minutes and 0 seconds to fill up the conical vessel.
Adding the time taken in minutes:
0 min + 0 min = 0 min
Therefore, it will take approximately 0 minutes to fill up the conical vessel.
However, none of the given options match the calculated time. Please check the question and options again.
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Water flows at a rate of 10 m per minute from a cylindrical pipe, 5 mm in diameter. How long will it take to fill up a conical vessel whose diameter of the base is 40 cm and depth is 24 cm?a)48 min 15 secb)51 min 12 secc)52 min 1 secd)55 minCorrect answer is option 'B'. Can you explain this answer?
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Water flows at a rate of 10 m per minute from a cylindrical pipe, 5 mm in diameter. How long will it take to fill up a conical vessel whose diameter of the base is 40 cm and depth is 24 cm?a)48 min 15 secb)51 min 12 secc)52 min 1 secd)55 minCorrect answer is option 'B'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Water flows at a rate of 10 m per minute from a cylindrical pipe, 5 mm in diameter. How long will it take to fill up a conical vessel whose diameter of the base is 40 cm and depth is 24 cm?a)48 min 15 secb)51 min 12 secc)52 min 1 secd)55 minCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Water flows at a rate of 10 m per minute from a cylindrical pipe, 5 mm in diameter. How long will it take to fill up a conical vessel whose diameter of the base is 40 cm and depth is 24 cm?a)48 min 15 secb)51 min 12 secc)52 min 1 secd)55 minCorrect answer is option 'B'. Can you explain this answer?.
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