Quant Exam > Quant Questions > Two cones have their heights in the ratio 1 :...
Start Learning for Free
Two cones have their heights in the ratio 1 : 2 and the diameters of their bases are in the ratio 2 :1. What will be the ratio of their volumes?
- a)4 : 1
- b)2 : 1
- c)3 : 2
- d)1 : 1
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Two cones have their heights in the ratio 1 : 2 and the diameters of t...
If the ratio of their diameters = 2 : 1, then the ratio of their radii will also be = 2 : 1
Let the radii of the broader cone = 2 and height be = 1
Then the radii of the smaller cone = 1 and height be = 2
Let the radii of the broader cone = 2 and height be = 1
Then the radii of the smaller cone = 1 and height be = 2
Most Upvoted Answer
Two cones have their heights in the ratio 1 : 2 and the diameters of t...
Given information:
- Heights of two cones are in the ratio of 1:2
- Diameters of their bases are in the ratio of 2:1
To find:
Ratio of their volumes
Solution:
Let the height of the first cone be h1 and the height of the second cone be h2.
Let the diameter of the base of the first cone be d1 and the diameter of the base of the second cone be d2.
Let the radius of the base of the first cone be r1 and the radius of the base of the second cone be r2.
From the given information, we know that:
h1 : h2 = 1 : 2
d1 : d2 = 2 : 1
We also know that the volume of a cone is given by:
V = (1/3)πr^2h
where r is the radius of the base and h is the height of the cone.
We can use the information about the diameters of the bases to find the ratio of the radii:
r1 = (d1/2) and r2 = (d2/2)
r1 : r2 = (d1/2) : (d2/2) = d1 : d2 = 2 : 1
Now, we can use the information about the heights to find the ratio of the volumes:
V1/V2 = (1/3)πr1^2h1 / (1/3)πr2^2h2
V1/V2 = r1^2h1 / r2^2h2
V1/V2 = [(d1/2)^2h1] / [(d2/2)^2h2]
V1/V2 = (d1^2/4)(h1/h2)(1/d2^2)
Substituting the given ratios:
V1/V2 = (2^2/4)(1/2)(1/1^2)
V1/V2 = 1/2
Therefore, the ratio of the volumes of the two cones is 2:1. Hence, option B is the correct answer.
- Heights of two cones are in the ratio of 1:2
- Diameters of their bases are in the ratio of 2:1
To find:
Ratio of their volumes
Solution:
Let the height of the first cone be h1 and the height of the second cone be h2.
Let the diameter of the base of the first cone be d1 and the diameter of the base of the second cone be d2.
Let the radius of the base of the first cone be r1 and the radius of the base of the second cone be r2.
From the given information, we know that:
h1 : h2 = 1 : 2
d1 : d2 = 2 : 1
We also know that the volume of a cone is given by:
V = (1/3)πr^2h
where r is the radius of the base and h is the height of the cone.
We can use the information about the diameters of the bases to find the ratio of the radii:
r1 = (d1/2) and r2 = (d2/2)
r1 : r2 = (d1/2) : (d2/2) = d1 : d2 = 2 : 1
Now, we can use the information about the heights to find the ratio of the volumes:
V1/V2 = (1/3)πr1^2h1 / (1/3)πr2^2h2
V1/V2 = r1^2h1 / r2^2h2
V1/V2 = [(d1/2)^2h1] / [(d2/2)^2h2]
V1/V2 = (d1^2/4)(h1/h2)(1/d2^2)
Substituting the given ratios:
V1/V2 = (2^2/4)(1/2)(1/1^2)
V1/V2 = 1/2
Therefore, the ratio of the volumes of the two cones is 2:1. Hence, option B is the correct answer.
Free Test
FREE
| Start Free Test |
Community Answer
Two cones have their heights in the ratio 1 : 2 and the diameters of t...
2:1
|
Explore Courses for Quant exam
|
|
Similar Quant Doubts
Question Description
Two cones have their heights in the ratio 1 : 2 and the diameters of their bases are in the ratio 2 :1. What will be the ratio of their volumes?a)4 : 1b)2 : 1c)3 : 2d)1 : 1Correct answer is option 'B'. Can you explain this answer? for Quant 2025 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about Two cones have their heights in the ratio 1 : 2 and the diameters of their bases are in the ratio 2 :1. What will be the ratio of their volumes?a)4 : 1b)2 : 1c)3 : 2d)1 : 1Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Quant 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two cones have their heights in the ratio 1 : 2 and the diameters of their bases are in the ratio 2 :1. What will be the ratio of their volumes?a)4 : 1b)2 : 1c)3 : 2d)1 : 1Correct answer is option 'B'. Can you explain this answer?.
Two cones have their heights in the ratio 1 : 2 and the diameters of their bases are in the ratio 2 :1. What will be the ratio of their volumes?a)4 : 1b)2 : 1c)3 : 2d)1 : 1Correct answer is option 'B'. Can you explain this answer? for Quant 2025 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about Two cones have their heights in the ratio 1 : 2 and the diameters of their bases are in the ratio 2 :1. What will be the ratio of their volumes?a)4 : 1b)2 : 1c)3 : 2d)1 : 1Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Quant 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two cones have their heights in the ratio 1 : 2 and the diameters of their bases are in the ratio 2 :1. What will be the ratio of their volumes?a)4 : 1b)2 : 1c)3 : 2d)1 : 1Correct answer is option 'B'. Can you explain this answer?.
Solutions for Two cones have their heights in the ratio 1 : 2 and the diameters of their bases are in the ratio 2 :1. What will be the ratio of their volumes?a)4 : 1b)2 : 1c)3 : 2d)1 : 1Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Quant.
Download more important topics, notes, lectures and mock test series for Quant Exam by signing up for free.
Here you can find the meaning of Two cones have their heights in the ratio 1 : 2 and the diameters of their bases are in the ratio 2 :1. What will be the ratio of their volumes?a)4 : 1b)2 : 1c)3 : 2d)1 : 1Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Two cones have their heights in the ratio 1 : 2 and the diameters of their bases are in the ratio 2 :1. What will be the ratio of their volumes?a)4 : 1b)2 : 1c)3 : 2d)1 : 1Correct answer is option 'B'. Can you explain this answer?, a detailed solution for Two cones have their heights in the ratio 1 : 2 and the diameters of their bases are in the ratio 2 :1. What will be the ratio of their volumes?a)4 : 1b)2 : 1c)3 : 2d)1 : 1Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of Two cones have their heights in the ratio 1 : 2 and the diameters of their bases are in the ratio 2 :1. What will be the ratio of their volumes?a)4 : 1b)2 : 1c)3 : 2d)1 : 1Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Two cones have their heights in the ratio 1 : 2 and the diameters of their bases are in the ratio 2 :1. What will be the ratio of their volumes?a)4 : 1b)2 : 1c)3 : 2d)1 : 1Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice Quant tests.
|
|
Explore Courses for Quant exam
|
|
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