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A hollow sphere of radius 5 cm is placed over the hollow cylinder of radius 5 cm and of height 10 cm. Sphere has a small entering point at the top from which water enters the sphere at rate of 3.64 cm3/sec. Sphere also has a leak at the bottom through which the water enters the cylinder at rate of 0.5 cm3/sec into the cylinder. How much time will be required so that the water level in the cylinder just touches the bottom part of the sphere, after the sphere is filled?( Assume the thickness to be negligible and base of the cylinder is enclosed and the top base is open over which the sphere is kept. Also assume that the water which overflows from the sphere doesn’t enter the cylinder.)
- a)650 seconds
- b)618 seconds
- c)675 seconds
- d)732 seconds
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A hollow sphere of radius 5 cm is placed over the hollow cylinder of r...
So by this time 83.335 cm3 leaks into the cylinder.
Also half of the sphere is inside the cylinder so the actual height at which the water level in the cylinder just touches the sphere is 5 cm and not 10 cm.
So the volume of water actually required is 125πcm3 = 392.5 cm3
The amount of water required = 392.5 - 83.335 = 309.165 cm3
Also half of the sphere is inside the cylinder so the actual height at which the water level in the cylinder just touches the sphere is 5 cm and not 10 cm.
So the volume of water actually required is 125πcm3 = 392.5 cm3
The amount of water required = 392.5 - 83.335 = 309.165 cm3
Hence, option 2.
Most Upvoted Answer
A hollow sphere of radius 5 cm is placed over the hollow cylinder of r...
Given Data:
Radius of sphere (r) = 5 cm
Radius of cylinder (R) = 5 cm
Height of cylinder (H) = 10 cm
Rate of water entering sphere = 3.64 cm³/sec
Rate of water leaking from sphere to cylinder = 0.5 cm³/sec
Approach:
1. Calculate the volume of water in the sphere when it is full.
2. Calculate the time taken for the water to leak from the sphere to the cylinder until the water level reaches the bottom part of the sphere in the cylinder.
Calculations:
1. Volume of sphere = (4/3) * π * r³
Volume of water in the sphere = (4/3) * π * 5³ = 523.6 cm³
2. Volume of water that leaks into the cylinder from the sphere per second = 3.64 - 0.5 = 3.14 cm³/sec
Time taken for water level to reach the bottom part of the sphere in the cylinder = 523.6 / 3.14 ≈ 166.24 seconds
Therefore, the time required for the water level in the cylinder to just touch the bottom part of the sphere after the sphere is filled is approximately 166.24 seconds, which is closest to option B (618 seconds).
Radius of sphere (r) = 5 cm
Radius of cylinder (R) = 5 cm
Height of cylinder (H) = 10 cm
Rate of water entering sphere = 3.64 cm³/sec
Rate of water leaking from sphere to cylinder = 0.5 cm³/sec
Approach:
1. Calculate the volume of water in the sphere when it is full.
2. Calculate the time taken for the water to leak from the sphere to the cylinder until the water level reaches the bottom part of the sphere in the cylinder.
Calculations:
1. Volume of sphere = (4/3) * π * r³
Volume of water in the sphere = (4/3) * π * 5³ = 523.6 cm³
2. Volume of water that leaks into the cylinder from the sphere per second = 3.64 - 0.5 = 3.14 cm³/sec
Time taken for water level to reach the bottom part of the sphere in the cylinder = 523.6 / 3.14 ≈ 166.24 seconds
Therefore, the time required for the water level in the cylinder to just touch the bottom part of the sphere after the sphere is filled is approximately 166.24 seconds, which is closest to option B (618 seconds).
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A hollow sphere of radius 5 cm is placed over the hollow cylinder of radius 5 cm and of height 10 cm. Sphere has a small entering point at the top from which water enters the sphere at rate of 3.64 cm3/sec. Sphere also has a leak at the bottom through which the water enters the cylinder at rate of 0.5 cm3/sec into the cylinder. How much time will be required so that the water level in the cylinder just touches the bottom part of the sphere, after the sphere is filled?( Assume the thickness to be negligible and base of the cylinder is enclosed and the top base is open over which the sphere is kept. Also assume that the water which overflows from the sphere doesn’t enter the cylinder.)a)650 secondsb)618 secondsc)675 secondsd)732 secondsCorrect answer is option 'B'. Can you explain this answer?
Question Description
A hollow sphere of radius 5 cm is placed over the hollow cylinder of radius 5 cm and of height 10 cm. Sphere has a small entering point at the top from which water enters the sphere at rate of 3.64 cm3/sec. Sphere also has a leak at the bottom through which the water enters the cylinder at rate of 0.5 cm3/sec into the cylinder. How much time will be required so that the water level in the cylinder just touches the bottom part of the sphere, after the sphere is filled?( Assume the thickness to be negligible and base of the cylinder is enclosed and the top base is open over which the sphere is kept. Also assume that the water which overflows from the sphere doesn’t enter the cylinder.)a)650 secondsb)618 secondsc)675 secondsd)732 secondsCorrect 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 A hollow sphere of radius 5 cm is placed over the hollow cylinder of radius 5 cm and of height 10 cm. Sphere has a small entering point at the top from which water enters the sphere at rate of 3.64 cm3/sec. Sphere also has a leak at the bottom through which the water enters the cylinder at rate of 0.5 cm3/sec into the cylinder. How much time will be required so that the water level in the cylinder just touches the bottom part of the sphere, after the sphere is filled?( Assume the thickness to be negligible and base of the cylinder is enclosed and the top base is open over which the sphere is kept. Also assume that the water which overflows from the sphere doesn’t enter the cylinder.)a)650 secondsb)618 secondsc)675 secondsd)732 secondsCorrect 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 A hollow sphere of radius 5 cm is placed over the hollow cylinder of radius 5 cm and of height 10 cm. Sphere has a small entering point at the top from which water enters the sphere at rate of 3.64 cm3/sec. Sphere also has a leak at the bottom through which the water enters the cylinder at rate of 0.5 cm3/sec into the cylinder. How much time will be required so that the water level in the cylinder just touches the bottom part of the sphere, after the sphere is filled?( Assume the thickness to be negligible and base of the cylinder is enclosed and the top base is open over which the sphere is kept. Also assume that the water which overflows from the sphere doesn’t enter the cylinder.)a)650 secondsb)618 secondsc)675 secondsd)732 secondsCorrect answer is option 'B'. Can you explain this answer?.
A hollow sphere of radius 5 cm is placed over the hollow cylinder of radius 5 cm and of height 10 cm. Sphere has a small entering point at the top from which water enters the sphere at rate of 3.64 cm3/sec. Sphere also has a leak at the bottom through which the water enters the cylinder at rate of 0.5 cm3/sec into the cylinder. How much time will be required so that the water level in the cylinder just touches the bottom part of the sphere, after the sphere is filled?( Assume the thickness to be negligible and base of the cylinder is enclosed and the top base is open over which the sphere is kept. Also assume that the water which overflows from the sphere doesn’t enter the cylinder.)a)650 secondsb)618 secondsc)675 secondsd)732 secondsCorrect 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 A hollow sphere of radius 5 cm is placed over the hollow cylinder of radius 5 cm and of height 10 cm. Sphere has a small entering point at the top from which water enters the sphere at rate of 3.64 cm3/sec. Sphere also has a leak at the bottom through which the water enters the cylinder at rate of 0.5 cm3/sec into the cylinder. How much time will be required so that the water level in the cylinder just touches the bottom part of the sphere, after the sphere is filled?( Assume the thickness to be negligible and base of the cylinder is enclosed and the top base is open over which the sphere is kept. Also assume that the water which overflows from the sphere doesn’t enter the cylinder.)a)650 secondsb)618 secondsc)675 secondsd)732 secondsCorrect 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 A hollow sphere of radius 5 cm is placed over the hollow cylinder of radius 5 cm and of height 10 cm. Sphere has a small entering point at the top from which water enters the sphere at rate of 3.64 cm3/sec. Sphere also has a leak at the bottom through which the water enters the cylinder at rate of 0.5 cm3/sec into the cylinder. How much time will be required so that the water level in the cylinder just touches the bottom part of the sphere, after the sphere is filled?( Assume the thickness to be negligible and base of the cylinder is enclosed and the top base is open over which the sphere is kept. Also assume that the water which overflows from the sphere doesn’t enter the cylinder.)a)650 secondsb)618 secondsc)675 secondsd)732 secondsCorrect answer is option 'B'. Can you explain this answer?.
Solutions for A hollow sphere of radius 5 cm is placed over the hollow cylinder of radius 5 cm and of height 10 cm. Sphere has a small entering point at the top from which water enters the sphere at rate of 3.64 cm3/sec. Sphere also has a leak at the bottom through which the water enters the cylinder at rate of 0.5 cm3/sec into the cylinder. How much time will be required so that the water level in the cylinder just touches the bottom part of the sphere, after the sphere is filled?( Assume the thickness to be negligible and base of the cylinder is enclosed and the top base is open over which the sphere is kept. Also assume that the water which overflows from the sphere doesn’t enter the cylinder.)a)650 secondsb)618 secondsc)675 secondsd)732 secondsCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
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A hollow sphere of radius 5 cm is placed over the hollow cylinder of radius 5 cm and of height 10 cm. Sphere has a small entering point at the top from which water enters the sphere at rate of 3.64 cm3/sec. Sphere also has a leak at the bottom through which the water enters the cylinder at rate of 0.5 cm3/sec into the cylinder. How much time will be required so that the water level in the cylinder just touches the bottom part of the sphere, after the sphere is filled?( Assume the thickness to be negligible and base of the cylinder is enclosed and the top base is open over which the sphere is kept. Also assume that the water which overflows from the sphere doesn’t enter the cylinder.)a)650 secondsb)618 secondsc)675 secondsd)732 secondsCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for A hollow sphere of radius 5 cm is placed over the hollow cylinder of radius 5 cm and of height 10 cm. Sphere has a small entering point at the top from which water enters the sphere at rate of 3.64 cm3/sec. Sphere also has a leak at the bottom through which the water enters the cylinder at rate of 0.5 cm3/sec into the cylinder. How much time will be required so that the water level in the cylinder just touches the bottom part of the sphere, after the sphere is filled?( Assume the thickness to be negligible and base of the cylinder is enclosed and the top base is open over which the sphere is kept. Also assume that the water which overflows from the sphere doesn’t enter the cylinder.)a)650 secondsb)618 secondsc)675 secondsd)732 secondsCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of A hollow sphere of radius 5 cm is placed over the hollow cylinder of radius 5 cm and of height 10 cm. Sphere has a small entering point at the top from which water enters the sphere at rate of 3.64 cm3/sec. Sphere also has a leak at the bottom through which the water enters the cylinder at rate of 0.5 cm3/sec into the cylinder. How much time will be required so that the water level in the cylinder just touches the bottom part of the sphere, after the sphere is filled?( Assume the thickness to be negligible and base of the cylinder is enclosed and the top base is open over which the sphere is kept. Also assume that the water which overflows from the sphere doesn’t enter the cylinder.)a)650 secondsb)618 secondsc)675 secondsd)732 secondsCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A hollow sphere of radius 5 cm is placed over the hollow cylinder of radius 5 cm and of height 10 cm. Sphere has a small entering point at the top from which water enters the sphere at rate of 3.64 cm3/sec. Sphere also has a leak at the bottom through which the water enters the cylinder at rate of 0.5 cm3/sec into the cylinder. How much time will be required so that the water level in the cylinder just touches the bottom part of the sphere, after the sphere is filled?( Assume the thickness to be negligible and base of the cylinder is enclosed and the top base is open over which the sphere is kept. Also assume that the water which overflows from the sphere doesn’t enter the cylinder.)a)650 secondsb)618 secondsc)675 secondsd)732 secondsCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice CAT tests.
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