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A man makes complete use of 405 cc of iron, 783 cc of aluminium, and 351 cc of copper to make a number of solid right circular cylinders of each type of metal. These cylinders have the same volume and each of these has radius 3 cm. If the total number of cylinders is to be kept at a minimum, then the total surface area of all these cylinders, in sq cm, is
(2019)
- a)8464π
- b)928π
- c)1026(1 – π)
- d)1044(4 + π)
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A man makes complete use of 405 cc of iron, 783 cc of aluminium, and 3...
To find the minimum number of cylinders, the volume of each of the cylinder must be HCF of 405, 783 and 351
HCF (405, 783, 351) = 27
Therefore, volume of each cylinder = 27cc
Hence number of cylinders of iron = 405 / 27 = 15
Number of cylinders of aluminium = 783 / 27 = 29
and number of cylinders of copper = 351 / 27 = 13
Therefore, the total number of a cylinders
= 15 + 29 + 13 = 57
Since, volume of each cylinder = 27cc
∴ πr2h = 27 ⇒ π × 32 × h = 27
⇒ h = 3 / π
Now, total surface area of each cylinder = 2πr (r + h)
∴ Total surface area of 57 cylinders
= 57 × 18(π + 1) sq. cm. = 1026 (π + 1)
HCF (405, 783, 351) = 27
Therefore, volume of each cylinder = 27cc
Hence number of cylinders of iron = 405 / 27 = 15
Number of cylinders of aluminium = 783 / 27 = 29
and number of cylinders of copper = 351 / 27 = 13
Therefore, the total number of a cylinders
= 15 + 29 + 13 = 57
Since, volume of each cylinder = 27cc
∴ πr2h = 27 ⇒ π × 32 × h = 27
⇒ h = 3 / π
Now, total surface area of each cylinder = 2πr (r + h)
∴ Total surface area of 57 cylinders
= 57 × 18(π + 1) sq. cm. = 1026 (π + 1)
Most Upvoted Answer
A man makes complete use of 405 cc of iron, 783 cc of aluminium, and 3...
To find the minimum number of cylinders, the volume of each of the cylinder must be HCF of 405, 783 and 351
HCF (405, 783, 351) = 27
Therefore, volume of each cylinder = 27cc
Hence number of cylinders of iron = 405 / 27 = 15
Number of cylinders of aluminium = 783 / 27 = 29
and number of cylinders of copper = 351 / 27 = 13
Therefore, the total number of a cylinders
= 15 + 29 + 13 = 57
Since, volume of each cylinder = 27cc
∴ πr2h = 27 ⇒ π × 32 × h = 27
⇒ h = 3 / π
Now, total surface area of each cylinder = 2πr (r + h)
∴ Total surface area of 57 cylinders
= 57 × 18(π + 1) sq. cm. = 1026 (π + 1)
HCF (405, 783, 351) = 27
Therefore, volume of each cylinder = 27cc
Hence number of cylinders of iron = 405 / 27 = 15
Number of cylinders of aluminium = 783 / 27 = 29
and number of cylinders of copper = 351 / 27 = 13
Therefore, the total number of a cylinders
= 15 + 29 + 13 = 57
Since, volume of each cylinder = 27cc
∴ πr2h = 27 ⇒ π × 32 × h = 27
⇒ h = 3 / π
Now, total surface area of each cylinder = 2πr (r + h)
∴ Total surface area of 57 cylinders
= 57 × 18(π + 1) sq. cm. = 1026 (π + 1)
Community Answer
A man makes complete use of 405 cc of iron, 783 cc of aluminium, and 3...
The volume of each cylinder is given by the formula V = πr^2h, where r is the radius and h is the height. Since the radius is 3 cm for all cylinders, the volume of each cylinder is simply 9πh.
Let's denote the number of cylinders made from iron, aluminium, and copper as n_iron, n_aluminium, and n_copper respectively.
From the given information, we have the following equations:
n_iron * 9πh_iron = 405 cc
n_aluminium * 9πh_aluminium = 783 cc
n_copper * 9πh_copper = 351 cc
We want to minimize the total number of cylinders, so we need to minimize the sum of n_iron, n_aluminium, and n_copper.
To do this, we can divide the equations above by the respective volumes to get:
n_iron = 405 / (9πh_iron)
n_aluminium = 783 / (9πh_aluminium)
n_copper = 351 / (9πh_copper)
Now, let's consider the surface area of each cylinder. The lateral surface area of a cylinder is given by the formula A = 2πrh. Since the radius is 3 cm for all cylinders, the lateral surface area simplifies to 6πh.
The total surface area of all the cylinders is given by the formula:
Total Surface Area = n_iron * 6πh_iron + n_aluminium * 6πh_aluminium + n_copper * 6πh_copper
Substituting the expressions for n_iron, n_aluminium, and n_copper from above, we get:
Total Surface Area = (405 / (9πh_iron)) * 6πh_iron + (783 / (9πh_aluminium)) * 6πh_aluminium + (351 / (9πh_copper)) * 6πh_copper
Simplifying, we find:
Total Surface Area = 2 * 405 + 2 * 783 + 2 * 351
Total Surface Area = 8466
Therefore, the total surface area of all these cylinders is 8466 sq cm. Answer choice (a) 8464 is the closest option.
Let's denote the number of cylinders made from iron, aluminium, and copper as n_iron, n_aluminium, and n_copper respectively.
From the given information, we have the following equations:
n_iron * 9πh_iron = 405 cc
n_aluminium * 9πh_aluminium = 783 cc
n_copper * 9πh_copper = 351 cc
We want to minimize the total number of cylinders, so we need to minimize the sum of n_iron, n_aluminium, and n_copper.
To do this, we can divide the equations above by the respective volumes to get:
n_iron = 405 / (9πh_iron)
n_aluminium = 783 / (9πh_aluminium)
n_copper = 351 / (9πh_copper)
Now, let's consider the surface area of each cylinder. The lateral surface area of a cylinder is given by the formula A = 2πrh. Since the radius is 3 cm for all cylinders, the lateral surface area simplifies to 6πh.
The total surface area of all the cylinders is given by the formula:
Total Surface Area = n_iron * 6πh_iron + n_aluminium * 6πh_aluminium + n_copper * 6πh_copper
Substituting the expressions for n_iron, n_aluminium, and n_copper from above, we get:
Total Surface Area = (405 / (9πh_iron)) * 6πh_iron + (783 / (9πh_aluminium)) * 6πh_aluminium + (351 / (9πh_copper)) * 6πh_copper
Simplifying, we find:
Total Surface Area = 2 * 405 + 2 * 783 + 2 * 351
Total Surface Area = 8466
Therefore, the total surface area of all these cylinders is 8466 sq cm. Answer choice (a) 8464 is the closest option.
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A man makes complete use of 405 cc of iron, 783 cc of aluminium, and 351 cc of copper to make a number of solid right circular cylinders of each type of metal. These cylinders have the same volume and each of these has radius 3 cm. If the total number of cylinders is to be kept at a minimum, then the total surface area of all these cylinders, in sq cm, is(2019)a)8464πb)928πc)1026(1 – π)d)1044(4 + π)Correct answer is option 'C'. Can you explain this answer?
Question Description
A man makes complete use of 405 cc of iron, 783 cc of aluminium, and 351 cc of copper to make a number of solid right circular cylinders of each type of metal. These cylinders have the same volume and each of these has radius 3 cm. If the total number of cylinders is to be kept at a minimum, then the total surface area of all these cylinders, in sq cm, is(2019)a)8464πb)928πc)1026(1 – π)d)1044(4 + π)Correct answer is option 'C'. 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 A man makes complete use of 405 cc of iron, 783 cc of aluminium, and 351 cc of copper to make a number of solid right circular cylinders of each type of metal. These cylinders have the same volume and each of these has radius 3 cm. If the total number of cylinders is to be kept at a minimum, then the total surface area of all these cylinders, in sq cm, is(2019)a)8464πb)928πc)1026(1 – π)d)1044(4 + π)Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A man makes complete use of 405 cc of iron, 783 cc of aluminium, and 351 cc of copper to make a number of solid right circular cylinders of each type of metal. These cylinders have the same volume and each of these has radius 3 cm. If the total number of cylinders is to be kept at a minimum, then the total surface area of all these cylinders, in sq cm, is(2019)a)8464πb)928πc)1026(1 – π)d)1044(4 + π)Correct answer is option 'C'. Can you explain this answer?.
A man makes complete use of 405 cc of iron, 783 cc of aluminium, and 351 cc of copper to make a number of solid right circular cylinders of each type of metal. These cylinders have the same volume and each of these has radius 3 cm. If the total number of cylinders is to be kept at a minimum, then the total surface area of all these cylinders, in sq cm, is(2019)a)8464πb)928πc)1026(1 – π)d)1044(4 + π)Correct answer is option 'C'. 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 A man makes complete use of 405 cc of iron, 783 cc of aluminium, and 351 cc of copper to make a number of solid right circular cylinders of each type of metal. These cylinders have the same volume and each of these has radius 3 cm. If the total number of cylinders is to be kept at a minimum, then the total surface area of all these cylinders, in sq cm, is(2019)a)8464πb)928πc)1026(1 – π)d)1044(4 + π)Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A man makes complete use of 405 cc of iron, 783 cc of aluminium, and 351 cc of copper to make a number of solid right circular cylinders of each type of metal. These cylinders have the same volume and each of these has radius 3 cm. If the total number of cylinders is to be kept at a minimum, then the total surface area of all these cylinders, in sq cm, is(2019)a)8464πb)928πc)1026(1 – π)d)1044(4 + π)Correct answer is option 'C'. Can you explain this answer?.
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