Class 10 Exam > Class 10 Questions > The radii of two cylinders are in the ratio 2...
Start Learning for Free
The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. What is the ratio of their volumes?
- a)20 : 27
- b)27 : 20
- c)9 : 4
- d)4 : 9
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
The radii of two cylinders are in the ratio 2 : 3 and their heights ar...
Given:
The ratio of the radii of two cylinders is 2:3.
The ratio of the heights of the two cylinders is 5:3.
To find:
The ratio of their volumes.
Solution:
Let's assume the radii of the cylinders to be 2x and 3x, and the heights to be 5y and 3y respectively.
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.
Volume of the first cylinder:
V1 = π(2x)^2(5y)
V1 = 4πx^2y
Volume of the second cylinder:
V2 = π(3x)^2(3y)
V2 = 9πx^2y
Ratio of their volumes:
V1 : V2 = (4πx^2y) : (9πx^2y)
V1 : V2 = 4x^2y : 9x^2y
Simplifying the ratio:
The common factors x^2 and y cancel out.
V1 : V2 = 4 : 9
Therefore, the ratio of the volumes of the two cylinders is 4:9, which is equivalent to 20:27.
Final Answer:
The ratio of the volumes of the two cylinders is 20:27. Hence, the correct option is (a) 20:27.
The ratio of the radii of two cylinders is 2:3.
The ratio of the heights of the two cylinders is 5:3.
To find:
The ratio of their volumes.
Solution:
Let's assume the radii of the cylinders to be 2x and 3x, and the heights to be 5y and 3y respectively.
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.
Volume of the first cylinder:
V1 = π(2x)^2(5y)
V1 = 4πx^2y
Volume of the second cylinder:
V2 = π(3x)^2(3y)
V2 = 9πx^2y
Ratio of their volumes:
V1 : V2 = (4πx^2y) : (9πx^2y)
V1 : V2 = 4x^2y : 9x^2y
Simplifying the ratio:
The common factors x^2 and y cancel out.
V1 : V2 = 4 : 9
Therefore, the ratio of the volumes of the two cylinders is 4:9, which is equivalent to 20:27.
Final Answer:
The ratio of the volumes of the two cylinders is 20:27. Hence, the correct option is (a) 20:27.
Free Test
FREE
| Start Free Test |
Community Answer
The radii of two cylinders are in the ratio 2 : 3 and their heights ar...
Let the radii of two cylinders are 2r, 3r and heights be 5h and 3h.
Ratio of their volumes
Ratio of their volumes
Attention Class 10 Students!
To make sure you are not studying endlessly, EduRev has designed Class 10 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 10.
|
Explore Courses for Class 10 exam
|
|
Top Courses for Class 10View all
The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. What is the ratio of their volumes?a)20 : 27b)27 : 20c)9 : 4d)4 : 9Correct answer is option 'A'. Can you explain this answer?
Question Description
The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. What is the ratio of their volumes?a)20 : 27b)27 : 20c)9 : 4d)4 : 9Correct answer is option 'A'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. What is the ratio of their volumes?a)20 : 27b)27 : 20c)9 : 4d)4 : 9Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. What is the ratio of their volumes?a)20 : 27b)27 : 20c)9 : 4d)4 : 9Correct answer is option 'A'. Can you explain this answer?.
The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. What is the ratio of their volumes?a)20 : 27b)27 : 20c)9 : 4d)4 : 9Correct answer is option 'A'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. What is the ratio of their volumes?a)20 : 27b)27 : 20c)9 : 4d)4 : 9Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. What is the ratio of their volumes?a)20 : 27b)27 : 20c)9 : 4d)4 : 9Correct answer is option 'A'. Can you explain this answer?.
Solutions for The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. What is the ratio of their volumes?a)20 : 27b)27 : 20c)9 : 4d)4 : 9Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 10.
Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free.
Here you can find the meaning of The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. What is the ratio of their volumes?a)20 : 27b)27 : 20c)9 : 4d)4 : 9Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. What is the ratio of their volumes?a)20 : 27b)27 : 20c)9 : 4d)4 : 9Correct answer is option 'A'. Can you explain this answer?, a detailed solution for The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. What is the ratio of their volumes?a)20 : 27b)27 : 20c)9 : 4d)4 : 9Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. What is the ratio of their volumes?a)20 : 27b)27 : 20c)9 : 4d)4 : 9Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. What is the ratio of their volumes?a)20 : 27b)27 : 20c)9 : 4d)4 : 9Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice Class 10 tests.
|
|
Explore Courses for Class 10 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup