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If the ratio of radius two Cylinders A and B are in the ratio of 2:1 and their heights are in the ratio of 2:1 respectively. The ratio of their total surface areas of Cylinder A to B is?
- a)2:1
- b)1:2
- c)1:4
- d)4:1
- e)Cannot be determined
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
If the ratio of radius two Cylinders A and B are in the ratio of 2:1 a...
Cylinder A: 2πr1 (r1 + h1)
Cylinder B: 2πr2 (r2 + h2)
r 1 /r 2 = 2:1; h 1 /h 2 = 2:1
T A /T B = 2πr1 (r1 + h1)/ 2πr2 (r2 + h2)
Cylinder B: 2πr2 (r2 + h2)
r 1 /r 2 = 2:1; h 1 /h 2 = 2:1
T A /T B = 2πr1 (r1 + h1)/ 2πr2 (r2 + h2)
Most Upvoted Answer
If the ratio of radius two Cylinders A and B are in the ratio of 2:1 a...
Given:
Ratio of radii of Cylinder A and Cylinder B = 2:1
Ratio of heights of Cylinder A and Cylinder B = 2:1
To find:
Ratio of total surface areas of Cylinder A to Cylinder B
Solution:
Let's assume the radius of Cylinder A as 2x and the radius of Cylinder B as x. Similarly, let's assume the height of Cylinder A as 2h and the height of Cylinder B as h.
Calculating the surface area of Cylinder A:
The total surface area of a cylinder is given by the formula:
Surface area = 2πrh + 2πr²
Substituting the values of radius and height of Cylinder A:
Surface area of Cylinder A = 2π(2x)(2h) + 2π(2x)²
Simplifying the expression:
Surface area of Cylinder A = 8πxh + 8πx² = 8π(xh + x²)
Calculating the surface area of Cylinder B:
Substituting the values of radius and height of Cylinder B:
Surface area of Cylinder B = 2π(x)(h) + 2π(x)²
Simplifying the expression:
Surface area of Cylinder B = 2πxh + 2πx²
Calculating the ratio of surface areas:
Ratio of surface areas of Cylinder A to Cylinder B = (Surface area of Cylinder A) / (Surface area of Cylinder B)
= (8π(xh + x²)) / (2πxh + 2πx²)
= 4(xh + x²) / (xh + x²)
= 4
Therefore, the ratio of the total surface areas of Cylinder A to Cylinder B is 4:1.
Answer:
The correct answer is option D) 4:1.
Ratio of radii of Cylinder A and Cylinder B = 2:1
Ratio of heights of Cylinder A and Cylinder B = 2:1
To find:
Ratio of total surface areas of Cylinder A to Cylinder B
Solution:
Let's assume the radius of Cylinder A as 2x and the radius of Cylinder B as x. Similarly, let's assume the height of Cylinder A as 2h and the height of Cylinder B as h.
Calculating the surface area of Cylinder A:
The total surface area of a cylinder is given by the formula:
Surface area = 2πrh + 2πr²
Substituting the values of radius and height of Cylinder A:
Surface area of Cylinder A = 2π(2x)(2h) + 2π(2x)²
Simplifying the expression:
Surface area of Cylinder A = 8πxh + 8πx² = 8π(xh + x²)
Calculating the surface area of Cylinder B:
Substituting the values of radius and height of Cylinder B:
Surface area of Cylinder B = 2π(x)(h) + 2π(x)²
Simplifying the expression:
Surface area of Cylinder B = 2πxh + 2πx²
Calculating the ratio of surface areas:
Ratio of surface areas of Cylinder A to Cylinder B = (Surface area of Cylinder A) / (Surface area of Cylinder B)
= (8π(xh + x²)) / (2πxh + 2πx²)
= 4(xh + x²) / (xh + x²)
= 4
Therefore, the ratio of the total surface areas of Cylinder A to Cylinder B is 4:1.
Answer:
The correct answer is option D) 4:1.
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If the ratio of radius two Cylinders A and B are in the ratio of 2:1 and their heights are in the ratio of 2:1 respectively. The ratio of their total surface areas of Cylinder A to B is?a)2:1b)1:2c)1:4d)4:1e)Cannot be determinedCorrect answer is option 'D'. Can you explain this answer?
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If the ratio of radius two Cylinders A and B are in the ratio of 2:1 and their heights are in the ratio of 2:1 respectively. The ratio of their total surface areas of Cylinder A to B is?a)2:1b)1:2c)1:4d)4:1e)Cannot be determinedCorrect answer is option 'D'. 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 If the ratio of radius two Cylinders A and B are in the ratio of 2:1 and their heights are in the ratio of 2:1 respectively. The ratio of their total surface areas of Cylinder A to B is?a)2:1b)1:2c)1:4d)4:1e)Cannot be determinedCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the ratio of radius two Cylinders A and B are in the ratio of 2:1 and their heights are in the ratio of 2:1 respectively. The ratio of their total surface areas of Cylinder A to B is?a)2:1b)1:2c)1:4d)4:1e)Cannot be determinedCorrect answer is option 'D'. Can you explain this answer?.
If the ratio of radius two Cylinders A and B are in the ratio of 2:1 and their heights are in the ratio of 2:1 respectively. The ratio of their total surface areas of Cylinder A to B is?a)2:1b)1:2c)1:4d)4:1e)Cannot be determinedCorrect answer is option 'D'. 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 If the ratio of radius two Cylinders A and B are in the ratio of 2:1 and their heights are in the ratio of 2:1 respectively. The ratio of their total surface areas of Cylinder A to B is?a)2:1b)1:2c)1:4d)4:1e)Cannot be determinedCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the ratio of radius two Cylinders A and B are in the ratio of 2:1 and their heights are in the ratio of 2:1 respectively. The ratio of their total surface areas of Cylinder A to B is?a)2:1b)1:2c)1:4d)4:1e)Cannot be determinedCorrect answer is option 'D'. Can you explain this answer?.
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If the ratio of radius two Cylinders A and B are in the ratio of 2:1 and their heights are in the ratio of 2:1 respectively. The ratio of their total surface areas of Cylinder A to B is?a)2:1b)1:2c)1:4d)4:1e)Cannot be determinedCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for If the ratio of radius two Cylinders A and B are in the ratio of 2:1 and their heights are in the ratio of 2:1 respectively. The ratio of their total surface areas of Cylinder A to B is?a)2:1b)1:2c)1:4d)4:1e)Cannot be determinedCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of If the ratio of radius two Cylinders A and B are in the ratio of 2:1 and their heights are in the ratio of 2:1 respectively. The ratio of their total surface areas of Cylinder A to B is?a)2:1b)1:2c)1:4d)4:1e)Cannot be determinedCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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