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A thirsty crow finds a cylindrical drum of height 12 units and radius 1 units, which has water upto a height of 8 units. Since the crow can only drink water from the brim of the drum, it is unable to drink the water right now. He therefore throws 120 spherical pebbles of diameter 0.5 units in the tumbler. How many more pebbles does he need to throw in the drum so that he can drink the water? Neglect the space between the pebbles.
- a)72
- b)120
- c)60
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A thirsty crow finds a cylindrical drum of height 12 units and radius ...
Let the increase in the height of water in the tumbler be h units because of the 120 pebbles of diameter 0.5 units that are dropped in the tumbler
∴ π x 12 x h = 120 x 4 / 3 x π x (1 / 4)3
∴ π x 12 x h = 120 x 4 / 3 x π x (1 / 4)3
h = 2.5 units
Height of the water in the drum after 120 pebbles are thrown = 8 + 2.5 = 10.5 units The crow still needs to raise the height of the water by 1.5 units.
Let n be the number of pebbles needed to raise the height of the water by 1.5 units.
∴ π x 12 x 1.5 = n x 4 / 3 x π x (1 / 4)3
Height of the water in the drum after 120 pebbles are thrown = 8 + 2.5 = 10.5 units The crow still needs to raise the height of the water by 1.5 units.
Let n be the number of pebbles needed to raise the height of the water by 1.5 units.
∴ π x 12 x 1.5 = n x 4 / 3 x π x (1 / 4)3
n = 72
Hence, option 1.
Most Upvoted Answer
A thirsty crow finds a cylindrical drum of height 12 units and radius ...
To solve this problem, we need to calculate the volume of water already present in the drum and compare it with the volume of water required by the crow to drink.
1. Calculating the volume of water already present in the drum:
Given: Height of the drum = 12 units
Radius of the drum = 1 unit
Height of the water in the drum = 8 units
The volume of water in the drum can be calculated using the formula for the volume of a cylinder:
Volume = π * r^2 * h
where r is the radius and h is the height.
Plugging in the values, we get:
Volume = π * 1^2 * 8
= 8π cubic units
2. Calculating the volume of each spherical pebble:
Given: Diameter of each pebble = 0.5 units
The volume of a sphere can be calculated using the formula:
Volume = (4/3) * π * r^3
where r is the radius.
Since the diameter is given, we need to divide it by 2 to get the radius.
Radius = 0.5/2 = 0.25 units
Plugging in the values, we get:
Volume = (4/3) * π * (0.25)^3
= (1/3) * π * 0.015625
= 0.005208333π cubic units
3. Calculating the total volume of the pebbles thrown in the drum:
Given: Number of pebbles thrown = 120
To find the total volume, we need to multiply the volume of each pebble by the number of pebbles:
Total volume = 0.005208333π * 120
= 0.625π cubic units
4. Calculating the remaining volume of water required by the crow:
Remaining volume = Volume of water required - Volume of water already present
= (12π - 8π) cubic units
= 4π cubic units
5. Calculating the number of additional pebbles required:
We know that the total volume of the pebbles thrown is 0.625π cubic units.
Let's assume the number of additional pebbles required is x.
Therefore, the total volume of the pebbles including the additional pebbles would be:
Total volume = (0.005208333π * 120) + (0.005208333π * x)
= 0.625π + (0.005208333π * x)
We need to find the value of x when the total volume is equal to the remaining volume required by the crow:
0.625π + (0.005208333π * x) = 4π
Simplifying the equation, we get:
0.005208333π * x = 4π - 0.625π
0.005208333π * x = 3.375π
x = 3.375/0.005208333
x = 648
Therefore, the crow needs to throw 648 - 120 = 528 more pebbles in the drum to be able to drink the water.
1. Calculating the volume of water already present in the drum:
Given: Height of the drum = 12 units
Radius of the drum = 1 unit
Height of the water in the drum = 8 units
The volume of water in the drum can be calculated using the formula for the volume of a cylinder:
Volume = π * r^2 * h
where r is the radius and h is the height.
Plugging in the values, we get:
Volume = π * 1^2 * 8
= 8π cubic units
2. Calculating the volume of each spherical pebble:
Given: Diameter of each pebble = 0.5 units
The volume of a sphere can be calculated using the formula:
Volume = (4/3) * π * r^3
where r is the radius.
Since the diameter is given, we need to divide it by 2 to get the radius.
Radius = 0.5/2 = 0.25 units
Plugging in the values, we get:
Volume = (4/3) * π * (0.25)^3
= (1/3) * π * 0.015625
= 0.005208333π cubic units
3. Calculating the total volume of the pebbles thrown in the drum:
Given: Number of pebbles thrown = 120
To find the total volume, we need to multiply the volume of each pebble by the number of pebbles:
Total volume = 0.005208333π * 120
= 0.625π cubic units
4. Calculating the remaining volume of water required by the crow:
Remaining volume = Volume of water required - Volume of water already present
= (12π - 8π) cubic units
= 4π cubic units
5. Calculating the number of additional pebbles required:
We know that the total volume of the pebbles thrown is 0.625π cubic units.
Let's assume the number of additional pebbles required is x.
Therefore, the total volume of the pebbles including the additional pebbles would be:
Total volume = (0.005208333π * 120) + (0.005208333π * x)
= 0.625π + (0.005208333π * x)
We need to find the value of x when the total volume is equal to the remaining volume required by the crow:
0.625π + (0.005208333π * x) = 4π
Simplifying the equation, we get:
0.005208333π * x = 4π - 0.625π
0.005208333π * x = 3.375π
x = 3.375/0.005208333
x = 648
Therefore, the crow needs to throw 648 - 120 = 528 more pebbles in the drum to be able to drink the water.
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A thirsty crow finds a cylindrical drum of height 12 units and radius 1 units, which has water upto a height of 8 units. Since the crow can only drink water from the brim of the drum, it is unable to drink the water right now. He therefore throws 120 spherical pebbles of diameter 0.5 units in the tumbler. How many more pebbles does he need to throw in the drum so that he can drink the water? Neglect the space between the pebbles.a)72b)120c)60d)None of theseCorrect answer is option 'A'. Can you explain this answer?
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A thirsty crow finds a cylindrical drum of height 12 units and radius 1 units, which has water upto a height of 8 units. Since the crow can only drink water from the brim of the drum, it is unable to drink the water right now. He therefore throws 120 spherical pebbles of diameter 0.5 units in the tumbler. How many more pebbles does he need to throw in the drum so that he can drink the water? Neglect the space between the pebbles.a)72b)120c)60d)None of theseCorrect answer is option 'A'. 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 thirsty crow finds a cylindrical drum of height 12 units and radius 1 units, which has water upto a height of 8 units. Since the crow can only drink water from the brim of the drum, it is unable to drink the water right now. He therefore throws 120 spherical pebbles of diameter 0.5 units in the tumbler. How many more pebbles does he need to throw in the drum so that he can drink the water? Neglect the space between the pebbles.a)72b)120c)60d)None of theseCorrect answer is option 'A'. 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 thirsty crow finds a cylindrical drum of height 12 units and radius 1 units, which has water upto a height of 8 units. Since the crow can only drink water from the brim of the drum, it is unable to drink the water right now. He therefore throws 120 spherical pebbles of diameter 0.5 units in the tumbler. How many more pebbles does he need to throw in the drum so that he can drink the water? Neglect the space between the pebbles.a)72b)120c)60d)None of theseCorrect answer is option 'A'. Can you explain this answer?.
A thirsty crow finds a cylindrical drum of height 12 units and radius 1 units, which has water upto a height of 8 units. Since the crow can only drink water from the brim of the drum, it is unable to drink the water right now. He therefore throws 120 spherical pebbles of diameter 0.5 units in the tumbler. How many more pebbles does he need to throw in the drum so that he can drink the water? Neglect the space between the pebbles.a)72b)120c)60d)None of theseCorrect answer is option 'A'. 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 thirsty crow finds a cylindrical drum of height 12 units and radius 1 units, which has water upto a height of 8 units. Since the crow can only drink water from the brim of the drum, it is unable to drink the water right now. He therefore throws 120 spherical pebbles of diameter 0.5 units in the tumbler. How many more pebbles does he need to throw in the drum so that he can drink the water? Neglect the space between the pebbles.a)72b)120c)60d)None of theseCorrect answer is option 'A'. 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 thirsty crow finds a cylindrical drum of height 12 units and radius 1 units, which has water upto a height of 8 units. Since the crow can only drink water from the brim of the drum, it is unable to drink the water right now. He therefore throws 120 spherical pebbles of diameter 0.5 units in the tumbler. How many more pebbles does he need to throw in the drum so that he can drink the water? Neglect the space between the pebbles.a)72b)120c)60d)None of theseCorrect answer is option 'A'. Can you explain this answer?.
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A thirsty crow finds a cylindrical drum of height 12 units and radius 1 units, which has water upto a height of 8 units. Since the crow can only drink water from the brim of the drum, it is unable to drink the water right now. He therefore throws 120 spherical pebbles of diameter 0.5 units in the tumbler. How many more pebbles does he need to throw in the drum so that he can drink the water? Neglect the space between the pebbles.a)72b)120c)60d)None of theseCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for A thirsty crow finds a cylindrical drum of height 12 units and radius 1 units, which has water upto a height of 8 units. Since the crow can only drink water from the brim of the drum, it is unable to drink the water right now. He therefore throws 120 spherical pebbles of diameter 0.5 units in the tumbler. How many more pebbles does he need to throw in the drum so that he can drink the water? Neglect the space between the pebbles.a)72b)120c)60d)None of theseCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of A thirsty crow finds a cylindrical drum of height 12 units and radius 1 units, which has water upto a height of 8 units. Since the crow can only drink water from the brim of the drum, it is unable to drink the water right now. He therefore throws 120 spherical pebbles of diameter 0.5 units in the tumbler. How many more pebbles does he need to throw in the drum so that he can drink the water? Neglect the space between the pebbles.a)72b)120c)60d)None of theseCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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