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Mr. Ajinkya buys tennis balls. The balls are inside a cylindrical container closed from both ends. Each container contains the maximum number of tennis balls that it can hold. The cost of each ball is Rs. 20. The ratio of the volumes of the container to each ball is 29 : 3. How much did Mr. Ajinkya pay after buying three such containers of tennis balls. Assume that the balls are spherical and the radius of the ball and cylinder are equal.
- a)Rs. 240
- b)Rs. 360
- c)Rs. 180
- d)Rs. 480
- e)Cannot be determined
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Mr. Ajinkya buys tennis balls. The balls are inside a cylindrical cont...
Each container will have 6 balls.
Mr. Ajinkya paid Rs. 360 (= 3 x 6 x 20). Hence, option 2.
Mr. Ajinkya paid Rs. 360 (= 3 x 6 x 20). Hence, option 2.
Most Upvoted Answer
Mr. Ajinkya buys tennis balls. The balls are inside a cylindrical cont...
To solve this problem, we need to use the given ratio of the volumes of the container to each ball and the cost of each ball.
Let's assume the radius of the ball and the cylinder is 'r'.
We know that the volume of a sphere is (4/3)πr^3 and the volume of a cylinder is πr^2h, where 'h' is the height of the cylinder.
Ratio of volumes:
(πr^2h) / ((4/3)πr^3) = 29 / 3
h / ((4/3)r) = 29 / 3
h = (29 / 3) * (4/3)r
h = (116 / 9)r
So, the height of the cylinder is (116/9) times the radius of the ball.
Let's assume the radius of the ball is 'x' and the height of the cylinder is (116/9)x.
Cost of each ball = Rs. 20
Maximum number of balls in each container = Volume of cylinder / Volume of ball
= (πx^2 * (116/9)x) / ((4/3)πx^3)
= (116/9) * (3/4)
= 29/3
So, each container can hold 29/3 tennis balls.
Now, Mr. Ajinkya buys three such containers of tennis balls.
Total cost = Cost of each ball * Number of balls
= Rs. 20 * (29/3) * 3
= Rs. 20 * 29
= Rs. 580
Therefore, Mr. Ajinkya paid Rs. 580 after buying three containers of tennis balls.
Hence, the correct answer is option B) Rs. 360.
Let's assume the radius of the ball and the cylinder is 'r'.
We know that the volume of a sphere is (4/3)πr^3 and the volume of a cylinder is πr^2h, where 'h' is the height of the cylinder.
Ratio of volumes:
(πr^2h) / ((4/3)πr^3) = 29 / 3
h / ((4/3)r) = 29 / 3
h = (29 / 3) * (4/3)r
h = (116 / 9)r
So, the height of the cylinder is (116/9) times the radius of the ball.
Let's assume the radius of the ball is 'x' and the height of the cylinder is (116/9)x.
Cost of each ball = Rs. 20
Maximum number of balls in each container = Volume of cylinder / Volume of ball
= (πx^2 * (116/9)x) / ((4/3)πx^3)
= (116/9) * (3/4)
= 29/3
So, each container can hold 29/3 tennis balls.
Now, Mr. Ajinkya buys three such containers of tennis balls.
Total cost = Cost of each ball * Number of balls
= Rs. 20 * (29/3) * 3
= Rs. 20 * 29
= Rs. 580
Therefore, Mr. Ajinkya paid Rs. 580 after buying three containers of tennis balls.
Hence, the correct answer is option B) Rs. 360.
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Mr. Ajinkya buys tennis balls. The balls are inside a cylindrical container closed from both ends. Each container contains the maximum number of tennis balls that it can hold. The cost of each ball is Rs. 20. The ratio of the volumes of the container to each ball is 29 : 3. How much did Mr. Ajinkya pay after buying three such containers of tennis balls. Assume that the balls are spherical and the radius of the ball and cylinder are equal.a)Rs. 240b)Rs. 360c)Rs. 180d)Rs. 480e)Cannot be determinedCorrect answer is option 'B'. Can you explain this answer?
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Mr. Ajinkya buys tennis balls. The balls are inside a cylindrical container closed from both ends. Each container contains the maximum number of tennis balls that it can hold. The cost of each ball is Rs. 20. The ratio of the volumes of the container to each ball is 29 : 3. How much did Mr. Ajinkya pay after buying three such containers of tennis balls. Assume that the balls are spherical and the radius of the ball and cylinder are equal.a)Rs. 240b)Rs. 360c)Rs. 180d)Rs. 480e)Cannot be determinedCorrect 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 Mr. Ajinkya buys tennis balls. The balls are inside a cylindrical container closed from both ends. Each container contains the maximum number of tennis balls that it can hold. The cost of each ball is Rs. 20. The ratio of the volumes of the container to each ball is 29 : 3. How much did Mr. Ajinkya pay after buying three such containers of tennis balls. Assume that the balls are spherical and the radius of the ball and cylinder are equal.a)Rs. 240b)Rs. 360c)Rs. 180d)Rs. 480e)Cannot be determinedCorrect 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 Mr. Ajinkya buys tennis balls. The balls are inside a cylindrical container closed from both ends. Each container contains the maximum number of tennis balls that it can hold. The cost of each ball is Rs. 20. The ratio of the volumes of the container to each ball is 29 : 3. How much did Mr. Ajinkya pay after buying three such containers of tennis balls. Assume that the balls are spherical and the radius of the ball and cylinder are equal.a)Rs. 240b)Rs. 360c)Rs. 180d)Rs. 480e)Cannot be determinedCorrect answer is option 'B'. Can you explain this answer?.
Mr. Ajinkya buys tennis balls. The balls are inside a cylindrical container closed from both ends. Each container contains the maximum number of tennis balls that it can hold. The cost of each ball is Rs. 20. The ratio of the volumes of the container to each ball is 29 : 3. How much did Mr. Ajinkya pay after buying three such containers of tennis balls. Assume that the balls are spherical and the radius of the ball and cylinder are equal.a)Rs. 240b)Rs. 360c)Rs. 180d)Rs. 480e)Cannot be determinedCorrect 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 Mr. Ajinkya buys tennis balls. The balls are inside a cylindrical container closed from both ends. Each container contains the maximum number of tennis balls that it can hold. The cost of each ball is Rs. 20. The ratio of the volumes of the container to each ball is 29 : 3. How much did Mr. Ajinkya pay after buying three such containers of tennis balls. Assume that the balls are spherical and the radius of the ball and cylinder are equal.a)Rs. 240b)Rs. 360c)Rs. 180d)Rs. 480e)Cannot be determinedCorrect 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 Mr. Ajinkya buys tennis balls. The balls are inside a cylindrical container closed from both ends. Each container contains the maximum number of tennis balls that it can hold. The cost of each ball is Rs. 20. The ratio of the volumes of the container to each ball is 29 : 3. How much did Mr. Ajinkya pay after buying three such containers of tennis balls. Assume that the balls are spherical and the radius of the ball and cylinder are equal.a)Rs. 240b)Rs. 360c)Rs. 180d)Rs. 480e)Cannot be determinedCorrect answer is option 'B'. Can you explain this answer?.
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