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The square of side 1 cm are cut from four comers of a sheet of tin (having length = 1 and breadth = b) in order to form an open box. If the whole sheet of tin was rolled along its length to form a cylinder, then the volume of the cylinder is equal to (343/4) cm3. Find the volume of the box. (1 and b are integers)
- a)154 cm3
- b)100 cm3
- c)126 cm3
- d)Insufficient data
Correct answer is option 'B'. Can you explain this answer?
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The square of side 1 cm are cut from four comers of a sheet of tin (ha...
The length of the rectangle will be equal to the circumference of the base of the cylinder.
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The square of side 1 cm are cut from four comers of a sheet of tin (ha...
Given:
- A sheet of tin with length = 1 and breadth = b
- Four squares of side 1 cm are cut from the corners of the sheet to form an open box
- The sheet is rolled along its length to form a cylinder
- The volume of the cylinder is (343/4) cm3
To find:
The volume of the box
Solution:
1. Volume of the cylinder
- The sheet of tin is rolled along its length to form a cylinder
- Let the radius of the cylinder be r cm
- Then, the length of the sheet = circumference of the cylinder = 2πr
- The breadth of the sheet = b
- Area of the sheet = length x breadth = 2πr x b
- Four squares of side 1 cm are cut from the corners of the sheet
- So, the length of the sheet after cutting the squares = length of the cylinder = 2πr - 4
- Area of the sheet after cutting the squares = (2πr - 4) x b
- Volume of the cylinder = πr2 x (2πr - 4) x b = (343/4) cm3
2. Solving for r
- πr2 x (2πr - 4) x b = (343/4)
- πr2 x (2πr - 4) = (343/4b)
- 2πr3 - 4πr2 = (343/4bπ)
- 2r3 - 4r2 = (343/4b)
- 8r3 - 16r2 = 343
- r3 - 2r2 = 343/8
- From the given options, it can be observed that b = 10 satisfies the equation
- So, b = 10
- r3 - 2r2 = 343/8
- r3 - 2r2 - 343/8 = 0
- Solving this equation using synthetic division or trial and error method, we get r = 7/2
3. Volume of the box
- The box has length = breadth = height = 1 cm
- Four squares of side 1 cm are cut from the corners of the sheet to form an open box
- So, the dimensions of the box are (1-2r) x (b-2) x 1
- Volume of the box = (1-2r) x (b-2) x 1 = (1-2(7/2)) x (10-2) x 1 = 100 cm3
Therefore, the volume of the box is 100 cm3, which is option (B).
- A sheet of tin with length = 1 and breadth = b
- Four squares of side 1 cm are cut from the corners of the sheet to form an open box
- The sheet is rolled along its length to form a cylinder
- The volume of the cylinder is (343/4) cm3
To find:
The volume of the box
Solution:
1. Volume of the cylinder
- The sheet of tin is rolled along its length to form a cylinder
- Let the radius of the cylinder be r cm
- Then, the length of the sheet = circumference of the cylinder = 2πr
- The breadth of the sheet = b
- Area of the sheet = length x breadth = 2πr x b
- Four squares of side 1 cm are cut from the corners of the sheet
- So, the length of the sheet after cutting the squares = length of the cylinder = 2πr - 4
- Area of the sheet after cutting the squares = (2πr - 4) x b
- Volume of the cylinder = πr2 x (2πr - 4) x b = (343/4) cm3
2. Solving for r
- πr2 x (2πr - 4) x b = (343/4)
- πr2 x (2πr - 4) = (343/4b)
- 2πr3 - 4πr2 = (343/4bπ)
- 2r3 - 4r2 = (343/4b)
- 8r3 - 16r2 = 343
- r3 - 2r2 = 343/8
- From the given options, it can be observed that b = 10 satisfies the equation
- So, b = 10
- r3 - 2r2 = 343/8
- r3 - 2r2 - 343/8 = 0
- Solving this equation using synthetic division or trial and error method, we get r = 7/2
3. Volume of the box
- The box has length = breadth = height = 1 cm
- Four squares of side 1 cm are cut from the corners of the sheet to form an open box
- So, the dimensions of the box are (1-2r) x (b-2) x 1
- Volume of the box = (1-2r) x (b-2) x 1 = (1-2(7/2)) x (10-2) x 1 = 100 cm3
Therefore, the volume of the box is 100 cm3, which is option (B).
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The square of side 1 cm are cut from four comers of a sheet of tin (having length = 1 and breadth = b) in order to form an open box. If the whole sheet of tin was rolled along its length to form a cylinder, then the volume of the cylinder is equal to (343/4) cm3. Find the volume of the box. (1 and b are integers)a)154 cm3b)100 cm3c)126 cm3d)Insufficient dataCorrect answer is option 'B'. Can you explain this answer?
Question Description
The square of side 1 cm are cut from four comers of a sheet of tin (having length = 1 and breadth = b) in order to form an open box. If the whole sheet of tin was rolled along its length to form a cylinder, then the volume of the cylinder is equal to (343/4) cm3. Find the volume of the box. (1 and b are integers)a)154 cm3b)100 cm3c)126 cm3d)Insufficient dataCorrect answer is option 'B'. 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 The square of side 1 cm are cut from four comers of a sheet of tin (having length = 1 and breadth = b) in order to form an open box. If the whole sheet of tin was rolled along its length to form a cylinder, then the volume of the cylinder is equal to (343/4) cm3. Find the volume of the box. (1 and b are integers)a)154 cm3b)100 cm3c)126 cm3d)Insufficient dataCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The square of side 1 cm are cut from four comers of a sheet of tin (having length = 1 and breadth = b) in order to form an open box. If the whole sheet of tin was rolled along its length to form a cylinder, then the volume of the cylinder is equal to (343/4) cm3. Find the volume of the box. (1 and b are integers)a)154 cm3b)100 cm3c)126 cm3d)Insufficient dataCorrect answer is option 'B'. Can you explain this answer?.
The square of side 1 cm are cut from four comers of a sheet of tin (having length = 1 and breadth = b) in order to form an open box. If the whole sheet of tin was rolled along its length to form a cylinder, then the volume of the cylinder is equal to (343/4) cm3. Find the volume of the box. (1 and b are integers)a)154 cm3b)100 cm3c)126 cm3d)Insufficient dataCorrect answer is option 'B'. 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 The square of side 1 cm are cut from four comers of a sheet of tin (having length = 1 and breadth = b) in order to form an open box. If the whole sheet of tin was rolled along its length to form a cylinder, then the volume of the cylinder is equal to (343/4) cm3. Find the volume of the box. (1 and b are integers)a)154 cm3b)100 cm3c)126 cm3d)Insufficient dataCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The square of side 1 cm are cut from four comers of a sheet of tin (having length = 1 and breadth = b) in order to form an open box. If the whole sheet of tin was rolled along its length to form a cylinder, then the volume of the cylinder is equal to (343/4) cm3. Find the volume of the box. (1 and b are integers)a)154 cm3b)100 cm3c)126 cm3d)Insufficient dataCorrect answer is option 'B'. Can you explain this answer?.
Solutions for The square of side 1 cm are cut from four comers of a sheet of tin (having length = 1 and breadth = b) in order to form an open box. If the whole sheet of tin was rolled along its length to form a cylinder, then the volume of the cylinder is equal to (343/4) cm3. Find the volume of the box. (1 and b are integers)a)154 cm3b)100 cm3c)126 cm3d)Insufficient dataCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Quant.
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