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Under the Indian Posts and Telegraph Act 1885, any package in the form of a right circular cylinder will not be accepted if the sum of its height and the diameter of its base exceeds 10 inches. The height (in inches) of a package of maximum volume that would be accepted is
- a)10/3
- b)20/3
- c)10
- d)20
Correct answer is option 'A'. Can you explain this answer?
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Under the Indian Posts and Telegraph Act 1885, any package in the form...
Volume is maximum when radius is equal to height.
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Under the Indian Posts and Telegraph Act 1885, any package in the form...
Explanation:
Given:
- According to the Indian Posts and Telegraph Act 1885, the sum of the height and the diameter of a right circular cylinder should not exceed 10 inches.
- We need to find the height of the cylinder with the maximum volume that would be accepted under this rule.
Formula for volume of a cylinder:
- The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height of the cylinder.
Expressing diameter in terms of radius:
- Since the sum of the height and the diameter should not exceed 10 inches, we can express the diameter in terms of radius as d = 2r.
- Therefore, the sum of the height and the diameter can be written as h + 2r ≤ 10.
Expressing height in terms of radius:
- We need to express the height in terms of the radius to determine the maximum volume of the cylinder.
- From the given condition, h + 2r ≤ 10, we can express the height as h = 10 - 2r.
Substitute height in volume formula:
- Substituting the expression for height in terms of radius into the formula for the volume of a cylinder, we get V = πr^2(10 - 2r).
Finding maximum volume:
- To find the maximum volume, we need to differentiate the volume formula with respect to r, set it equal to zero, and solve for r.
- Differentiating the volume formula and setting it to zero, we get dV/dr = 0 ⇒ 20πr - 6πr^2 = 0 ⇒ r(20 - 6r) = 0.
- Solving for r, we get r = 0 or r = 20/6 = 10/3.
Calculating maximum height:
- Since the height is h = 10 - 2r, we can substitute r = 10/3 to find the maximum height.
- Therefore, h = 10 - 2(10/3) = 10/3 inches.
Conclusion:
- The height of a package of maximum volume that would be accepted under the given condition is 10/3 inches. Hence, the correct answer is option 'A'.
Given:
- According to the Indian Posts and Telegraph Act 1885, the sum of the height and the diameter of a right circular cylinder should not exceed 10 inches.
- We need to find the height of the cylinder with the maximum volume that would be accepted under this rule.
Formula for volume of a cylinder:
- The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height of the cylinder.
Expressing diameter in terms of radius:
- Since the sum of the height and the diameter should not exceed 10 inches, we can express the diameter in terms of radius as d = 2r.
- Therefore, the sum of the height and the diameter can be written as h + 2r ≤ 10.
Expressing height in terms of radius:
- We need to express the height in terms of the radius to determine the maximum volume of the cylinder.
- From the given condition, h + 2r ≤ 10, we can express the height as h = 10 - 2r.
Substitute height in volume formula:
- Substituting the expression for height in terms of radius into the formula for the volume of a cylinder, we get V = πr^2(10 - 2r).
Finding maximum volume:
- To find the maximum volume, we need to differentiate the volume formula with respect to r, set it equal to zero, and solve for r.
- Differentiating the volume formula and setting it to zero, we get dV/dr = 0 ⇒ 20πr - 6πr^2 = 0 ⇒ r(20 - 6r) = 0.
- Solving for r, we get r = 0 or r = 20/6 = 10/3.
Calculating maximum height:
- Since the height is h = 10 - 2r, we can substitute r = 10/3 to find the maximum height.
- Therefore, h = 10 - 2(10/3) = 10/3 inches.
Conclusion:
- The height of a package of maximum volume that would be accepted under the given condition is 10/3 inches. Hence, the correct answer is option 'A'.
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Under the Indian Posts and Telegraph Act 1885, any package in the form of a right circular cylinder will not be accepted if the sum of its height and the diameter of its base exceeds 10 inches. The height (in inches) of a package of maximum volume that would be accepted isa)10/3b)20/3c)10d)20Correct answer is option 'A'. Can you explain this answer?
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Under the Indian Posts and Telegraph Act 1885, any package in the form of a right circular cylinder will not be accepted if the sum of its height and the diameter of its base exceeds 10 inches. The height (in inches) of a package of maximum volume that would be accepted isa)10/3b)20/3c)10d)20Correct answer is option 'A'. 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 Under the Indian Posts and Telegraph Act 1885, any package in the form of a right circular cylinder will not be accepted if the sum of its height and the diameter of its base exceeds 10 inches. The height (in inches) of a package of maximum volume that would be accepted isa)10/3b)20/3c)10d)20Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Under the Indian Posts and Telegraph Act 1885, any package in the form of a right circular cylinder will not be accepted if the sum of its height and the diameter of its base exceeds 10 inches. The height (in inches) of a package of maximum volume that would be accepted isa)10/3b)20/3c)10d)20Correct answer is option 'A'. Can you explain this answer?.
Under the Indian Posts and Telegraph Act 1885, any package in the form of a right circular cylinder will not be accepted if the sum of its height and the diameter of its base exceeds 10 inches. The height (in inches) of a package of maximum volume that would be accepted isa)10/3b)20/3c)10d)20Correct answer is option 'A'. 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 Under the Indian Posts and Telegraph Act 1885, any package in the form of a right circular cylinder will not be accepted if the sum of its height and the diameter of its base exceeds 10 inches. The height (in inches) of a package of maximum volume that would be accepted isa)10/3b)20/3c)10d)20Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Under the Indian Posts and Telegraph Act 1885, any package in the form of a right circular cylinder will not be accepted if the sum of its height and the diameter of its base exceeds 10 inches. The height (in inches) of a package of maximum volume that would be accepted isa)10/3b)20/3c)10d)20Correct answer is option 'A'. Can you explain this answer?.
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