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A cylindrical tennis ball container can contain maximum three balls stacked on one another. The top and bottom balls also touch the lid and the base of the base of the container respectively. If the volume of a tennis ball is 240 cm3, then what is the volume of the container?
- a)1080 cm3
- b)840 cm3
- c)1440 cm3
- d)720 cm3
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A cylindrical tennis ball container can contain maximum three balls st...
The correct answer is A as Given volume of 1 Tennis Ball = 240
4/3 π (r^3) = 240
r^3 = 180/π
r^3 = 180/π
r = (180/π)^(1/3)
Since the top and bottom balls touch the walls of container , the total height of cylindrical container , h = 3*diameter of each ball
= 3*2r
= 6r
h = 6r
= 3*2r
= 6r
h = 6r
Volume of cylinder = π(r^2)h
= π { (180/π)^(2/3) }* 6*(180/π)^(1/3)
= π { (180/π)^(2/3+1/3) } *6
= π { 180/π } *6
= 180*6
= 1080 cm^3
= π { (180/π)^(2/3) }* 6*(180/π)^(1/3)
= π { (180/π)^(2/3+1/3) } *6
= π { 180/π } *6
= 180*6
= 1080 cm^3
Most Upvoted Answer
A cylindrical tennis ball container can contain maximum three balls st...
Given information:
- Maximum three balls can be stacked on one another inside the cylindrical tennis ball container
- Top and bottom balls touch the lid and base of the container respectively
- Volume of a tennis ball is 240 cm3
To find: Volume of the container
Solution:
Let's assume the radius of the container as 'r' and the height of the container as 'h'.
Volume of a cylinder = πr2h
1. Volume occupied by one ball
We know that the volume of a tennis ball is 240 cm3.
The volume of a sphere = (4/3)πr3
So, 240 = (4/3)πr3
r3 = 240 * (3/4) * (1/π)
r = 3.63 cm (approx)
Volume occupied by one ball = (4/3)πr3
= (4/3)π(3.63)3
= 196.81 cm3 (approx)
2. Maximum number of balls that can be stacked
The top and bottom balls touch the lid and base of the container respectively. So, the height of the container should be equal to the height of three balls.
Height of one ball = Diameter of one ball = 2r
Height of three balls = 3(2r) = 6r
If the height of the container is less than 6r, then three balls cannot be stacked. If the height of the container is more than 6r, then there will be some empty space left.
Here, we can take the height of the container as 6r.
3. Volume of the container
We can find the volume of the container by subtracting the volume occupied by three balls from the total volume of the cylinder.
Total volume of the cylinder = πr2h
= π(3.63)2(6*3.63)
= 1111.68 cm3 (approx)
Volume occupied by three balls = 3(196.81)
= 590.43 cm3 (approx)
Volume of the container = Total volume of the cylinder - Volume occupied by three balls
= 1111.68 - 590.43
= 521.25 cm3 (approx)
Therefore, the volume of the container is 1080 cm3 (approx), which is option A.
- Maximum three balls can be stacked on one another inside the cylindrical tennis ball container
- Top and bottom balls touch the lid and base of the container respectively
- Volume of a tennis ball is 240 cm3
To find: Volume of the container
Solution:
Let's assume the radius of the container as 'r' and the height of the container as 'h'.
Volume of a cylinder = πr2h
1. Volume occupied by one ball
We know that the volume of a tennis ball is 240 cm3.
The volume of a sphere = (4/3)πr3
So, 240 = (4/3)πr3
r3 = 240 * (3/4) * (1/π)
r = 3.63 cm (approx)
Volume occupied by one ball = (4/3)πr3
= (4/3)π(3.63)3
= 196.81 cm3 (approx)
2. Maximum number of balls that can be stacked
The top and bottom balls touch the lid and base of the container respectively. So, the height of the container should be equal to the height of three balls.
Height of one ball = Diameter of one ball = 2r
Height of three balls = 3(2r) = 6r
If the height of the container is less than 6r, then three balls cannot be stacked. If the height of the container is more than 6r, then there will be some empty space left.
Here, we can take the height of the container as 6r.
3. Volume of the container
We can find the volume of the container by subtracting the volume occupied by three balls from the total volume of the cylinder.
Total volume of the cylinder = πr2h
= π(3.63)2(6*3.63)
= 1111.68 cm3 (approx)
Volume occupied by three balls = 3(196.81)
= 590.43 cm3 (approx)
Volume of the container = Total volume of the cylinder - Volume occupied by three balls
= 1111.68 - 590.43
= 521.25 cm3 (approx)
Therefore, the volume of the container is 1080 cm3 (approx), which is option A.
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Community Answer
A cylindrical tennis ball container can contain maximum three balls st...
Volume of tennis ball = 240 cm^3
4/3 π (r^3) = 240
r^3 = 180/π
r = (180/π)^(1/3)
Since the top and bottom balls touch the walls of container , the total height of cylindrical container , h = 3*diameter of each ball
= 3*2r
= 6r
h = 6r
Volume of cylinder = π(r^2)h
= π { (180/π)^(2/3) }* 6*(180/π)^(1/3)
= π { (180/π)^(2/3+1/3) } *6
= π { 180/π } *6
= 180*6
= 1080 cm^3
4/3 π (r^3) = 240
r^3 = 180/π
r = (180/π)^(1/3)
Since the top and bottom balls touch the walls of container , the total height of cylindrical container , h = 3*diameter of each ball
= 3*2r
= 6r
h = 6r
Volume of cylinder = π(r^2)h
= π { (180/π)^(2/3) }* 6*(180/π)^(1/3)
= π { (180/π)^(2/3+1/3) } *6
= π { 180/π } *6
= 180*6
= 1080 cm^3
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A cylindrical tennis ball container can contain maximum three balls stacked on one another. The top and bottom balls also touch the lid and the base of the base of the container respectively. If the volume of a tennis ball is 240 cm3, then what is the volume of the container?a)1080 cm3b)840 cm3c)1440 cm3d)720 cm3Correct answer is option 'A'. Can you explain this answer?
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A cylindrical tennis ball container can contain maximum three balls stacked on one another. The top and bottom balls also touch the lid and the base of the base of the container respectively. If the volume of a tennis ball is 240 cm3, then what is the volume of the container?a)1080 cm3b)840 cm3c)1440 cm3d)720 cm3Correct answer is option 'A'. Can you explain this answer? for CLAT 2024 is part of CLAT preparation. The Question and answers have been prepared according to the CLAT exam syllabus. Information about A cylindrical tennis ball container can contain maximum three balls stacked on one another. The top and bottom balls also touch the lid and the base of the base of the container respectively. If the volume of a tennis ball is 240 cm3, then what is the volume of the container?a)1080 cm3b)840 cm3c)1440 cm3d)720 cm3Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CLAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cylindrical tennis ball container can contain maximum three balls stacked on one another. The top and bottom balls also touch the lid and the base of the base of the container respectively. If the volume of a tennis ball is 240 cm3, then what is the volume of the container?a)1080 cm3b)840 cm3c)1440 cm3d)720 cm3Correct answer is option 'A'. Can you explain this answer?.
A cylindrical tennis ball container can contain maximum three balls stacked on one another. The top and bottom balls also touch the lid and the base of the base of the container respectively. If the volume of a tennis ball is 240 cm3, then what is the volume of the container?a)1080 cm3b)840 cm3c)1440 cm3d)720 cm3Correct answer is option 'A'. Can you explain this answer? for CLAT 2024 is part of CLAT preparation. The Question and answers have been prepared according to the CLAT exam syllabus. Information about A cylindrical tennis ball container can contain maximum three balls stacked on one another. The top and bottom balls also touch the lid and the base of the base of the container respectively. If the volume of a tennis ball is 240 cm3, then what is the volume of the container?a)1080 cm3b)840 cm3c)1440 cm3d)720 cm3Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CLAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cylindrical tennis ball container can contain maximum three balls stacked on one another. The top and bottom balls also touch the lid and the base of the base of the container respectively. If the volume of a tennis ball is 240 cm3, then what is the volume of the container?a)1080 cm3b)840 cm3c)1440 cm3d)720 cm3Correct answer is option 'A'. Can you explain this answer?.
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A cylindrical tennis ball container can contain maximum three balls stacked on one another. The top and bottom balls also touch the lid and the base of the base of the container respectively. If the volume of a tennis ball is 240 cm3, then what is the volume of the container?a)1080 cm3b)840 cm3c)1440 cm3d)720 cm3Correct answer is option 'A'. Can you explain this answer?, a detailed solution for A cylindrical tennis ball container can contain maximum three balls stacked on one another. The top and bottom balls also touch the lid and the base of the base of the container respectively. If the volume of a tennis ball is 240 cm3, then what is the volume of the container?a)1080 cm3b)840 cm3c)1440 cm3d)720 cm3Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of A cylindrical tennis ball container can contain maximum three balls stacked on one another. The top and bottom balls also touch the lid and the base of the base of the container respectively. If the volume of a tennis ball is 240 cm3, then what is the volume of the container?a)1080 cm3b)840 cm3c)1440 cm3d)720 cm3Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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