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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 ...
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
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The number of iron cylinders = 405/27 = 15
The number of aluminium cylinders = 783/27 = 29
The number of copper cylinders = 315/27 = 13
15*πr2h= 405
15*π9*h= 405
πh = 3
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*(2πrh + 2πr2)
=57(2*3*3 + 2*9*π)
=1026(1 + π)
Most Upvoted Answer
A man makes complete use of 405 cc of iron, 783 cc of aluminium, and ...
To minimize the total number of cylinders, we need to ensure that the volumes of iron, aluminium, and copper used are all equal. Let's denote the common volume as V.
1. Volume of a cylinder:
The formula to calculate the volume of a cylinder is given by V = πr^2h, where r is the radius and h is the height of the cylinder. In this case, the radius is given as 3 cm.
2. Volume of iron:
Let's assume the number of iron cylinders is n. Therefore, the volume of iron used is Viron = nπ(3^2)h.
3. Volume of aluminium:
Similarly, assuming the number of aluminium cylinders is m, the volume of aluminium used is Valuminium = mπ(3^2)h.
4. Volume of copper:
Assuming the number of copper cylinders is p, the volume of copper used is Vcopper = pπ(3^2)h.
Since the volumes of iron, aluminium, and copper used are equal, we have the following equation:
nπ(3^2)h = mπ(3^2)h = pπ(3^2)h
Canceling out the common factors, we get:
n = m = p
5. Total surface area of the cylinders:
The formula to calculate the total surface area of a cylinder is given by A = 2πrh + 2πr^2. In this case, the height is not mentioned, so we can assume it to be 1 cm for simplicity.
The total surface area of iron cylinders is:
SAiron = 2π(3)(1) + 2π(3^2) = 6π + 18π = 24π
Similarly, the total surface area of aluminium cylinders is SAaluminium = 24π, and the total surface area of copper cylinders is SAcopper = 24π.
Since the total number of cylinders should be minimized, we need to find the minimum value of n (or m or p) for which the volumes of iron, aluminium, and copper are equal.
To find the minimum value, we need to find the highest common factor of 405, 783, and 351.
The highest common factor of 405, 783, and 351 is 27.
Therefore, the total number of cylinders is 27, and the total surface area of all these cylinders is 27 * 24π = 648π.
Hence, the correct answer is option A) 1026(1 π).
1. Volume of a cylinder:
The formula to calculate the volume of a cylinder is given by V = πr^2h, where r is the radius and h is the height of the cylinder. In this case, the radius is given as 3 cm.
2. Volume of iron:
Let's assume the number of iron cylinders is n. Therefore, the volume of iron used is Viron = nπ(3^2)h.
3. Volume of aluminium:
Similarly, assuming the number of aluminium cylinders is m, the volume of aluminium used is Valuminium = mπ(3^2)h.
4. Volume of copper:
Assuming the number of copper cylinders is p, the volume of copper used is Vcopper = pπ(3^2)h.
Since the volumes of iron, aluminium, and copper used are equal, we have the following equation:
nπ(3^2)h = mπ(3^2)h = pπ(3^2)h
Canceling out the common factors, we get:
n = m = p
5. Total surface area of the cylinders:
The formula to calculate the total surface area of a cylinder is given by A = 2πrh + 2πr^2. In this case, the height is not mentioned, so we can assume it to be 1 cm for simplicity.
The total surface area of iron cylinders is:
SAiron = 2π(3)(1) + 2π(3^2) = 6π + 18π = 24π
Similarly, the total surface area of aluminium cylinders is SAaluminium = 24π, and the total surface area of copper cylinders is SAcopper = 24π.
Since the total number of cylinders should be minimized, we need to find the minimum value of n (or m or p) for which the volumes of iron, aluminium, and copper are equal.
To find the minimum value, we need to find the highest common factor of 405, 783, and 351.
The highest common factor of 405, 783, and 351 is 27.
Therefore, the total number of cylinders is 27, and the total surface area of all these cylinders is 27 * 24π = 648π.
Hence, the correct answer is option A) 1026(1 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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