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Concentrated orange juice comes inside a cylinder tube with a radius of 2.5 inches and a height of 15 inches. The tubes are packed into wooden boxes, each with dimensions of 11 inches by 10 inches by 31 inches. How many tubes of concentrated orange juice, at the most, can fit into 3 wooden boxes?
- a)24
- b)28
- c)36
- d)42
- e)48
Correct answer is option 'A'. Can you explain this answer?
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Concentrated orange juice comes inside a cylinder tube with a radius o...
The best answer is A.
You want to waste as little amount of space as possible, therefore make the height of the box 11 and fit 4 boxes at the bottom so you lose only 1 inch of margin at the top and on one of the sides.
You can see that 8 tubes can fit into one box thus 24 tubes fit into 3 boxes.
Most Upvoted Answer
Concentrated orange juice comes inside a cylinder tube with a radius o...
Given:
Radius of the cylinder tube = 2.5 inches
Height of the cylinder tube = 15 inches
Dimensions of the wooden box = 11 inches by 10 inches by 31 inches
To find:
The maximum number of tubes of concentrated orange juice that can fit into 3 wooden boxes.
Solution:
1. Calculate the volume of the cylinder tube:
The volume of a cylinder can be calculated using the formula V = πr²h, where V is the volume, r is the radius, and h is the height.
In this case, the radius of the cylinder tube is 2.5 inches and the height is 15 inches.
So, the volume of the cylinder tube is V = π(2.5)²(15) = 94.25π cubic inches.
2. Calculate the volume of the wooden box:
The volume of a rectangular box can be calculated using the formula V = lwh, where V is the volume, l is the length, w is the width, and h is the height.
In this case, the dimensions of the wooden box are 11 inches by 10 inches by 31 inches.
So, the volume of the wooden box is V = (11)(10)(31) = 3410 cubic inches.
3. Determine the maximum number of tubes that can fit into a wooden box:
To calculate the maximum number of tubes that can fit into a wooden box, divide the volume of the wooden box by the volume of a single tube.
In this case, the volume of the wooden box is 3410 cubic inches and the volume of a single tube is 94.25π cubic inches.
So, the maximum number of tubes that can fit into a wooden box is 3410 / (94.25π) = approximately 11.5 tubes.
4. Determine the maximum number of tubes that can fit into 3 wooden boxes:
To calculate the maximum number of tubes that can fit into 3 wooden boxes, multiply the maximum number of tubes that can fit into a single wooden box by 3.
In this case, the maximum number of tubes that can fit into a single wooden box is approximately 11.5 tubes.
So, the maximum number of tubes that can fit into 3 wooden boxes is 11.5 * 3 = 34.5 tubes.
5. Since we cannot have a fraction of a tube, the maximum number of tubes that can fit into 3 wooden boxes is the largest whole number less than or equal to 34.5, which is 34.
Therefore, the maximum number of tubes of concentrated orange juice that can fit into 3 wooden boxes is 34, which is option (A).
Radius of the cylinder tube = 2.5 inches
Height of the cylinder tube = 15 inches
Dimensions of the wooden box = 11 inches by 10 inches by 31 inches
To find:
The maximum number of tubes of concentrated orange juice that can fit into 3 wooden boxes.
Solution:
1. Calculate the volume of the cylinder tube:
The volume of a cylinder can be calculated using the formula V = πr²h, where V is the volume, r is the radius, and h is the height.
In this case, the radius of the cylinder tube is 2.5 inches and the height is 15 inches.
So, the volume of the cylinder tube is V = π(2.5)²(15) = 94.25π cubic inches.
2. Calculate the volume of the wooden box:
The volume of a rectangular box can be calculated using the formula V = lwh, where V is the volume, l is the length, w is the width, and h is the height.
In this case, the dimensions of the wooden box are 11 inches by 10 inches by 31 inches.
So, the volume of the wooden box is V = (11)(10)(31) = 3410 cubic inches.
3. Determine the maximum number of tubes that can fit into a wooden box:
To calculate the maximum number of tubes that can fit into a wooden box, divide the volume of the wooden box by the volume of a single tube.
In this case, the volume of the wooden box is 3410 cubic inches and the volume of a single tube is 94.25π cubic inches.
So, the maximum number of tubes that can fit into a wooden box is 3410 / (94.25π) = approximately 11.5 tubes.
4. Determine the maximum number of tubes that can fit into 3 wooden boxes:
To calculate the maximum number of tubes that can fit into 3 wooden boxes, multiply the maximum number of tubes that can fit into a single wooden box by 3.
In this case, the maximum number of tubes that can fit into a single wooden box is approximately 11.5 tubes.
So, the maximum number of tubes that can fit into 3 wooden boxes is 11.5 * 3 = 34.5 tubes.
5. Since we cannot have a fraction of a tube, the maximum number of tubes that can fit into 3 wooden boxes is the largest whole number less than or equal to 34.5, which is 34.
Therefore, the maximum number of tubes of concentrated orange juice that can fit into 3 wooden boxes is 34, which is option (A).
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Concentrated orange juice comes inside a cylinder tube with a radius of 2.5 inches and a height of 15 inches. The tubes are packed into wooden boxes, each with dimensions of 11 inches by 10 inches by 31 inches. How many tubes of concentrated orange juice, at the most, can fit into 3 wooden boxes?a)24b)28c)36d)42e)48Correct answer is option 'A'. Can you explain this answer?
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Concentrated orange juice comes inside a cylinder tube with a radius of 2.5 inches and a height of 15 inches. The tubes are packed into wooden boxes, each with dimensions of 11 inches by 10 inches by 31 inches. How many tubes of concentrated orange juice, at the most, can fit into 3 wooden boxes?a)24b)28c)36d)42e)48Correct answer is option 'A'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Concentrated orange juice comes inside a cylinder tube with a radius of 2.5 inches and a height of 15 inches. The tubes are packed into wooden boxes, each with dimensions of 11 inches by 10 inches by 31 inches. How many tubes of concentrated orange juice, at the most, can fit into 3 wooden boxes?a)24b)28c)36d)42e)48Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Concentrated orange juice comes inside a cylinder tube with a radius of 2.5 inches and a height of 15 inches. The tubes are packed into wooden boxes, each with dimensions of 11 inches by 10 inches by 31 inches. How many tubes of concentrated orange juice, at the most, can fit into 3 wooden boxes?a)24b)28c)36d)42e)48Correct answer is option 'A'. Can you explain this answer?.
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