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Cylindrical cans of cricket balls are to be packed in a box. Each can has a radius of 7 cm and height of 30 cm. Dimension of the box is l = 76 cm, b = 46 cm, h = 45 cm. What is the maximum number of cans that can fit in the box?
- a)15
- b)17
- c)22
- d)21
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Cylindrical cans of cricket balls are to be packed in a box. Each can ...
This question requires a good deal of visualization. Since, both the box and cans are hard solids, simply dividing the volume won’t work because the shape can’t be deformed.
Each cylindrical can has a diameter of 14 cm and while they are kept erect in the box will occupy height of 30 cm
Number of such cans that can be placed in a row
Number of such rows that can be placed
Thus 5 x 3 = 15 cans can be placed in an erect position.
However, height of box = 45cm and only 30 cm has been utilized so far
Remaining height = 15 cm > 14 cm (Diameter of the can)
So, some cans can be placed horizontally on the base.
Number of cans in horizontal row
Number of such rows
∴ 2 x 3 = 6 cans can be placed horizontally
∴ Maximum number of cans = 15+6 = 21
Choice (D) is therefore, the correct answer.
Each cylindrical can has a diameter of 14 cm and while they are kept erect in the box will occupy height of 30 cm
Number of such cans that can be placed in a row
Number of such rows that can be placed
Thus 5 x 3 = 15 cans can be placed in an erect position.
However, height of box = 45cm and only 30 cm has been utilized so far
Remaining height = 15 cm > 14 cm (Diameter of the can)
So, some cans can be placed horizontally on the base.
Number of cans in horizontal row
Number of such rows
∴ 2 x 3 = 6 cans can be placed horizontally
∴ Maximum number of cans = 15+6 = 21
Choice (D) is therefore, the correct answer.
Most Upvoted Answer
Cylindrical cans of cricket balls are to be packed in a box. Each can ...
Given:
Radius of each can, r = 7 cm
Height of each can, h = 30 cm
Length of the box, l = 76 cm
Breadth of the box, b = 46 cm
Height of the box, h = 45 cm
To find: Maximum number of cans that can fit in the box
Solution:
Volume of one can = πr²h
= π(7)²(30)
= 4410π cm³
Volume of the box = lbh
= 76 × 46 × 45
= 155160 cm³
Number of cans that can fit in the box = Volume of the box/Volume of one can
= 155160/4410π
≈ 111.6
Therefore, the maximum number of cans that can fit in the box is the largest integer less than or equal to 111.6, which is 111.
Now, let's see if we can fit 111 cans in the box.
If we place the cans in a rectangular pattern, with the height of the box being the height of the cans, we can fit 4 cans in the length, 2 cans in the breadth, and 15 cans in the height. This gives a total of 4 × 2 × 15 = 120 cans, which is more than the maximum number of cans that can fit in the box.
Therefore, we need to adjust the pattern to fit 111 cans in the box. We can fit 3 cans in the length, 2 cans in the breadth, and 18 cans in the height. This gives a total of 3 × 2 × 18 = 108 cans. We can then add 3 more cans on top of the first layer, giving a total of 111 cans.
Therefore, the maximum number of cans that can fit in the box is 111, which is closest to option (d) 21.
Radius of each can, r = 7 cm
Height of each can, h = 30 cm
Length of the box, l = 76 cm
Breadth of the box, b = 46 cm
Height of the box, h = 45 cm
To find: Maximum number of cans that can fit in the box
Solution:
Volume of one can = πr²h
= π(7)²(30)
= 4410π cm³
Volume of the box = lbh
= 76 × 46 × 45
= 155160 cm³
Number of cans that can fit in the box = Volume of the box/Volume of one can
= 155160/4410π
≈ 111.6
Therefore, the maximum number of cans that can fit in the box is the largest integer less than or equal to 111.6, which is 111.
Now, let's see if we can fit 111 cans in the box.
If we place the cans in a rectangular pattern, with the height of the box being the height of the cans, we can fit 4 cans in the length, 2 cans in the breadth, and 15 cans in the height. This gives a total of 4 × 2 × 15 = 120 cans, which is more than the maximum number of cans that can fit in the box.
Therefore, we need to adjust the pattern to fit 111 cans in the box. We can fit 3 cans in the length, 2 cans in the breadth, and 18 cans in the height. This gives a total of 3 × 2 × 18 = 108 cans. We can then add 3 more cans on top of the first layer, giving a total of 111 cans.
Therefore, the maximum number of cans that can fit in the box is 111, which is closest to option (d) 21.
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Community Answer
Cylindrical cans of cricket balls are to be packed in a box. Each can ...
This question requires a good deal of visualization. Since, both the box and cans are hard solids, simply dividing the volume won’t work because the shape can’t be deformed.
Each cylindrical can has a diameter of 14 cm and while they are kept erect in the box will occupy height of 30 cm
Number of such cans that can be placed in a row
Number of such rows that can be placed
Thus 5 x 3 = 15 cans can be placed in an erect position.
However, height of box = 45cm and only 30 cm has been utilized so far
Remaining height = 15 cm > 14 cm (Diameter of the can)
So, some cans can be placed horizontally on the base.
Number of cans in horizontal row
Number of such rows
∴ 2 x 3 = 6 cans can be placed horizontally
∴ Maximum number of cans = 15+6 = 21
Choice (D) is therefore, the correct answer.
Each cylindrical can has a diameter of 14 cm and while they are kept erect in the box will occupy height of 30 cm
Number of such cans that can be placed in a row
Number of such rows that can be placed
Thus 5 x 3 = 15 cans can be placed in an erect position.
However, height of box = 45cm and only 30 cm has been utilized so far
Remaining height = 15 cm > 14 cm (Diameter of the can)
So, some cans can be placed horizontally on the base.
Number of cans in horizontal row
Number of such rows
∴ 2 x 3 = 6 cans can be placed horizontally
∴ Maximum number of cans = 15+6 = 21
Choice (D) is therefore, the correct answer.
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Cylindrical cans of cricket balls are to be packed in a box. Each can has a radius of 7 cm and height of 30 cm. Dimension of the box is l = 76 cm, b = 46 cm, h = 45 cm. What is the maximum number of cans that can fit in the box?a)15b)17c)22d)21Correct answer is option 'D'. Can you explain this answer?
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Cylindrical cans of cricket balls are to be packed in a box. Each can has a radius of 7 cm and height of 30 cm. Dimension of the box is l = 76 cm, b = 46 cm, h = 45 cm. What is the maximum number of cans that can fit in the box?a)15b)17c)22d)21Correct answer is option 'D'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about Cylindrical cans of cricket balls are to be packed in a box. Each can has a radius of 7 cm and height of 30 cm. Dimension of the box is l = 76 cm, b = 46 cm, h = 45 cm. What is the maximum number of cans that can fit in the box?a)15b)17c)22d)21Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Cylindrical cans of cricket balls are to be packed in a box. Each can has a radius of 7 cm and height of 30 cm. Dimension of the box is l = 76 cm, b = 46 cm, h = 45 cm. What is the maximum number of cans that can fit in the box?a)15b)17c)22d)21Correct answer is option 'D'. Can you explain this answer?.
Cylindrical cans of cricket balls are to be packed in a box. Each can has a radius of 7 cm and height of 30 cm. Dimension of the box is l = 76 cm, b = 46 cm, h = 45 cm. What is the maximum number of cans that can fit in the box?a)15b)17c)22d)21Correct answer is option 'D'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about Cylindrical cans of cricket balls are to be packed in a box. Each can has a radius of 7 cm and height of 30 cm. Dimension of the box is l = 76 cm, b = 46 cm, h = 45 cm. What is the maximum number of cans that can fit in the box?a)15b)17c)22d)21Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Cylindrical cans of cricket balls are to be packed in a box. Each can has a radius of 7 cm and height of 30 cm. Dimension of the box is l = 76 cm, b = 46 cm, h = 45 cm. What is the maximum number of cans that can fit in the box?a)15b)17c)22d)21Correct answer is option 'D'. Can you explain this answer?.
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