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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
- a)1026(1 + π)
- b)8464π
- c)928π
- d)1044(4 + π)
Correct answer is option 'A'. 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...
It is given that the volume of all the cylinders is the same, so the volume of each cylinder = HCF of (405, 783, 351) =27
The number of iron cylinders =
= 15
The number of aluminium cylinders =
= 29
The number of copper cylinders =
= 13
Now we have to calculate the total surface area of all the cylinders
Total number of cylinders = 15+29+13 = 57 Total surface area of the cylinder =
=57(2*3*3 + 2*9* )
= 1026(1 + π)
The number of iron cylinders =
= 15The number of aluminium cylinders =
= 29The number of copper cylinders =
= 13 Now we have to calculate the total surface area of all the cylinders
Total number of cylinders = 15+29+13 = 57 Total surface area of the cylinder =
=57(2*3*3 + 2*9* )
= 1026(1 + π)
Most Upvoted Answer
A man makes complete use of 405 cc of iron, 783 cc of aluminium, and 3...
The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height. Since all the cylinders have the same volume, we can set up the following equations:
V_iron = πr^2h_iron
V_aluminium = πr^2h_aluminium
V_copper = πr^2h_copper
We are given that the radius of each cylinder is 3 cm, so we can simplify the equations:
V_iron = 9πh_iron
V_aluminium = 9πh_aluminium
V_copper = 9πh_copper
Since the total volume of iron used is 405 cc, the total volume of aluminium used is 783 cc, and the total volume of copper used is 351 cc, we can write the following equations:
405 = 9πh_iron
783 = 9πh_aluminium
351 = 9πh_copper
Solving these equations for h_iron, h_aluminium, and h_copper, we find:
h_iron = 45/π
h_aluminium = 87/π
h_copper = 39/π
The total surface area of all the cylinders can be calculated using the formula A = 2πrh + 2πr^2. Since all the cylinders have the same radius, we can simplify the equation:
A_total = 2πr(h_iron + h_aluminium + h_copper) + 2πr^2(number of cylinders)
Substituting the given values, we have:
A_total = 2π(3)((45/π) + (87/π) + (39/π)) + 2π(3)^2(number of cylinders)
A_total = 2(3)(45 + 87 + 39)π + 2(3)^2(number of cylinders)
A_total = 468π + 18(number of cylinders)
To minimize the total surface area, we need to minimize the number of cylinders. Since the total volume of all the cylinders is fixed, we can minimize the number of cylinders by maximizing their height. In this case, the maximum height is the height of the cylinder with the smallest volume, which is the cylinder made of copper. Therefore, the total surface area is minimized when all the cylinders are made of copper.
Substituting h_copper into the equation for A_total, we have:
A_total = 468π + 18(number of cylinders)
A_total = 468π + 18(351/π)
A_total = 468π + 18(351/π)
A_total = 468π + 18(351/π)
A_total = 468π + 6318/π
To find the value of A_total, we need to know the value of π.
V_iron = πr^2h_iron
V_aluminium = πr^2h_aluminium
V_copper = πr^2h_copper
We are given that the radius of each cylinder is 3 cm, so we can simplify the equations:
V_iron = 9πh_iron
V_aluminium = 9πh_aluminium
V_copper = 9πh_copper
Since the total volume of iron used is 405 cc, the total volume of aluminium used is 783 cc, and the total volume of copper used is 351 cc, we can write the following equations:
405 = 9πh_iron
783 = 9πh_aluminium
351 = 9πh_copper
Solving these equations for h_iron, h_aluminium, and h_copper, we find:
h_iron = 45/π
h_aluminium = 87/π
h_copper = 39/π
The total surface area of all the cylinders can be calculated using the formula A = 2πrh + 2πr^2. Since all the cylinders have the same radius, we can simplify the equation:
A_total = 2πr(h_iron + h_aluminium + h_copper) + 2πr^2(number of cylinders)
Substituting the given values, we have:
A_total = 2π(3)((45/π) + (87/π) + (39/π)) + 2π(3)^2(number of cylinders)
A_total = 2(3)(45 + 87 + 39)π + 2(3)^2(number of cylinders)
A_total = 468π + 18(number of cylinders)
To minimize the total surface area, we need to minimize the number of cylinders. Since the total volume of all the cylinders is fixed, we can minimize the number of cylinders by maximizing their height. In this case, the maximum height is the height of the cylinder with the smallest volume, which is the cylinder made of copper. Therefore, the total surface area is minimized when all the cylinders are made of copper.
Substituting h_copper into the equation for A_total, we have:
A_total = 468π + 18(number of cylinders)
A_total = 468π + 18(351/π)
A_total = 468π + 18(351/π)
A_total = 468π + 18(351/π)
A_total = 468π + 6318/π
To find the value of A_total, we need to know the value of π.
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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, isa)1026(1 + π)b)8464πc)928πd)1044(4 + π)Correct answer is option 'A'. Can you explain this answer?
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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, isa)1026(1 + π)b)8464πc)928πd)1044(4 + π)Correct answer is option 'A'. 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, isa)1026(1 + π)b)8464πc)928πd)1044(4 + π)Correct answer is option 'A'. 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, isa)1026(1 + π)b)8464πc)928πd)1044(4 + π)Correct answer is option 'A'. 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, isa)1026(1 + π)b)8464πc)928πd)1044(4 + π)Correct answer is option 'A'. 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, isa)1026(1 + π)b)8464πc)928πd)1044(4 + π)Correct answer is option 'A'. 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, isa)1026(1 + π)b)8464πc)928πd)1044(4 + π)Correct answer is option 'A'. Can you explain this answer?.
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