Quant Exam > Quant Questions > A right circular cone has height H and radius...
Start Learning for Free
A right circular cone has height H and radius R. A small cone is cut off at the top by a plane parallel to the base. At what height above the base the section has been made?
Statement (I): H = 20 cm
Statement (II): Volume of small cone: volume of large cone : 1:15
Statement (I): H = 20 cm
Statement (II): Volume of small cone: volume of large cone : 1:15
- a)If the question can be answered with statement I alone but not statement II alone, or can be answered with statement II alone but not statement I alone.
- b)If the question cannot be answered with statement I alone or with statement II alone, but can be answered if both statements are used together.
- c)If the question can be answered with either statement alone.
- d)If the question cannot be answered with the information provided.
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
A right circular cone has height H and radius R. A small cone is cut o...
From statement I, we know that the height of the initial cone is 20cm. However, nothing is said about the small cone. Hence, we cannot answer the question using statement A. So, we can eliminate choices (A) and (D).
We are down to choices (A), (B) or (D).
From Statement II, we know that the ratio of the volume of the small cone to that of the large cone is 1 : 15.
i.e. *π*r2*h : *π*R2*H is 1 : 15 (r is the base radius of the smaller cone and h is the height of the smaller cone)
or r2 * h : R2 * H is 1 : 15
From this information, we will not be able to find the answer to h. Hence, we can eliminate choice (A).
Combining the information in the two statements:
When a section is made the two cones are similar triangles. so =
R =
We know H = 20
h = * r
i.e., h3 = H3. Substituting H = 20, we can get the value for h.
Choice (B) is therefore, the correct answer.
Correct Answer: If the question cannot be answered with statement I alone or with statement II alone, but can be answered if both statements are used together.
Most Upvoted Answer
A right circular cone has height H and radius R. A small cone is cut o...
Given:
- A right circular cone with height H and radius R.
- A small cone is cut off at the top by a plane parallel to the base.
- We need to find the height above the base where the section has been made.
Statement (I): H = 20 cm
Statement (II): Volume of small cone: volume of large cone : 1:15
To find the height above the base where the section has been made, we need to know the ratio of the height of the small cone to the height of the large cone.
Using Statement (I) alone:
- We only know the height of the large cone, which is H = 20 cm.
- We cannot determine the ratio of the heights of the small and large cones, so we cannot answer the question.
- Therefore, option (a) is not correct.
Using Statement (II) alone:
- We know that the ratio of the volume of the small cone to the volume of the large cone is 1:15.
- Let the height of the small cone be h. Then the height of the large cone is (H - h).
- The ratio of the volumes of the small and large cones is (1/3) * pi * R^2 * h : (1/3) * pi * R^2 * (H - h).
- Simplifying, we get h : (H - h) = 1 : 15.
- Solving for h, we get h = H/16.
- Therefore, we know the height of the small cone.
- Using this height, we can determine the height above the base where the section has been made.
- Therefore, option (b) is correct.
Using both statements together:
- We know the height of the large cone (H) from Statement (I) and the ratio of the volumes of the small and large cones from Statement (II).
- Using the same method as in the previous case, we can determine the height of the small cone and answer the question.
- Therefore, option (b) is correct.
Conclusion:
- The question can be answered using Statement (II) alone or using both statements together.
- Therefore, the correct option is (b).
- A right circular cone with height H and radius R.
- A small cone is cut off at the top by a plane parallel to the base.
- We need to find the height above the base where the section has been made.
Statement (I): H = 20 cm
Statement (II): Volume of small cone: volume of large cone : 1:15
To find the height above the base where the section has been made, we need to know the ratio of the height of the small cone to the height of the large cone.
Using Statement (I) alone:
- We only know the height of the large cone, which is H = 20 cm.
- We cannot determine the ratio of the heights of the small and large cones, so we cannot answer the question.
- Therefore, option (a) is not correct.
Using Statement (II) alone:
- We know that the ratio of the volume of the small cone to the volume of the large cone is 1:15.
- Let the height of the small cone be h. Then the height of the large cone is (H - h).
- The ratio of the volumes of the small and large cones is (1/3) * pi * R^2 * h : (1/3) * pi * R^2 * (H - h).
- Simplifying, we get h : (H - h) = 1 : 15.
- Solving for h, we get h = H/16.
- Therefore, we know the height of the small cone.
- Using this height, we can determine the height above the base where the section has been made.
- Therefore, option (b) is correct.
Using both statements together:
- We know the height of the large cone (H) from Statement (I) and the ratio of the volumes of the small and large cones from Statement (II).
- Using the same method as in the previous case, we can determine the height of the small cone and answer the question.
- Therefore, option (b) is correct.
Conclusion:
- The question can be answered using Statement (II) alone or using both statements together.
- Therefore, the correct option is (b).
|
Explore Courses for Quant exam
|
|
Similar Quant Doubts
A right circular cone has height H and radius R. A small cone is cut off at the top by a plane parallel to the base. At what height above the base the section has been made?Statement (I): H = 20 cmStatement (II): Volume of small cone: volume of large cone : 1:15a)If the question can be answered with statement I alone but not statement II alone, or can be answered with statement II alone but not statement I alone.b)If the question cannot be answered with statement I alone or with statement II alone, but can be answered if both statements are used together.c)If the question can be answered with either statement alone.d)If the question cannot be answered with the information provided.Correct answer is option 'B'. Can you explain this answer?
Question Description
A right circular cone has height H and radius R. A small cone is cut off at the top by a plane parallel to the base. At what height above the base the section has been made?Statement (I): H = 20 cmStatement (II): Volume of small cone: volume of large cone : 1:15a)If the question can be answered with statement I alone but not statement II alone, or can be answered with statement II alone but not statement I alone.b)If the question cannot be answered with statement I alone or with statement II alone, but can be answered if both statements are used together.c)If the question can be answered with either statement alone.d)If the question cannot be answered with the information provided.Correct answer is option 'B'. 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 A right circular cone has height H and radius R. A small cone is cut off at the top by a plane parallel to the base. At what height above the base the section has been made?Statement (I): H = 20 cmStatement (II): Volume of small cone: volume of large cone : 1:15a)If the question can be answered with statement I alone but not statement II alone, or can be answered with statement II alone but not statement I alone.b)If the question cannot be answered with statement I alone or with statement II alone, but can be answered if both statements are used together.c)If the question can be answered with either statement alone.d)If the question cannot be answered with the information provided.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A right circular cone has height H and radius R. A small cone is cut off at the top by a plane parallel to the base. At what height above the base the section has been made?Statement (I): H = 20 cmStatement (II): Volume of small cone: volume of large cone : 1:15a)If the question can be answered with statement I alone but not statement II alone, or can be answered with statement II alone but not statement I alone.b)If the question cannot be answered with statement I alone or with statement II alone, but can be answered if both statements are used together.c)If the question can be answered with either statement alone.d)If the question cannot be answered with the information provided.Correct answer is option 'B'. Can you explain this answer?.
A right circular cone has height H and radius R. A small cone is cut off at the top by a plane parallel to the base. At what height above the base the section has been made?Statement (I): H = 20 cmStatement (II): Volume of small cone: volume of large cone : 1:15a)If the question can be answered with statement I alone but not statement II alone, or can be answered with statement II alone but not statement I alone.b)If the question cannot be answered with statement I alone or with statement II alone, but can be answered if both statements are used together.c)If the question can be answered with either statement alone.d)If the question cannot be answered with the information provided.Correct answer is option 'B'. 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 A right circular cone has height H and radius R. A small cone is cut off at the top by a plane parallel to the base. At what height above the base the section has been made?Statement (I): H = 20 cmStatement (II): Volume of small cone: volume of large cone : 1:15a)If the question can be answered with statement I alone but not statement II alone, or can be answered with statement II alone but not statement I alone.b)If the question cannot be answered with statement I alone or with statement II alone, but can be answered if both statements are used together.c)If the question can be answered with either statement alone.d)If the question cannot be answered with the information provided.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A right circular cone has height H and radius R. A small cone is cut off at the top by a plane parallel to the base. At what height above the base the section has been made?Statement (I): H = 20 cmStatement (II): Volume of small cone: volume of large cone : 1:15a)If the question can be answered with statement I alone but not statement II alone, or can be answered with statement II alone but not statement I alone.b)If the question cannot be answered with statement I alone or with statement II alone, but can be answered if both statements are used together.c)If the question can be answered with either statement alone.d)If the question cannot be answered with the information provided.Correct answer is option 'B'. Can you explain this answer?.
Solutions for A right circular cone has height H and radius R. A small cone is cut off at the top by a plane parallel to the base. At what height above the base the section has been made?Statement (I): H = 20 cmStatement (II): Volume of small cone: volume of large cone : 1:15a)If the question can be answered with statement I alone but not statement II alone, or can be answered with statement II alone but not statement I alone.b)If the question cannot be answered with statement I alone or with statement II alone, but can be answered if both statements are used together.c)If the question can be answered with either statement alone.d)If the question cannot be answered with the information provided.Correct 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 A right circular cone has height H and radius R. A small cone is cut off at the top by a plane parallel to the base. At what height above the base the section has been made?Statement (I): H = 20 cmStatement (II): Volume of small cone: volume of large cone : 1:15a)If the question can be answered with statement I alone but not statement II alone, or can be answered with statement II alone but not statement I alone.b)If the question cannot be answered with statement I alone or with statement II alone, but can be answered if both statements are used together.c)If the question can be answered with either statement alone.d)If the question cannot be answered with the information provided.Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A right circular cone has height H and radius R. A small cone is cut off at the top by a plane parallel to the base. At what height above the base the section has been made?Statement (I): H = 20 cmStatement (II): Volume of small cone: volume of large cone : 1:15a)If the question can be answered with statement I alone but not statement II alone, or can be answered with statement II alone but not statement I alone.b)If the question cannot be answered with statement I alone or with statement II alone, but can be answered if both statements are used together.c)If the question can be answered with either statement alone.d)If the question cannot be answered with the information provided.Correct answer is option 'B'. Can you explain this answer?, a detailed solution for A right circular cone has height H and radius R. A small cone is cut off at the top by a plane parallel to the base. At what height above the base the section has been made?Statement (I): H = 20 cmStatement (II): Volume of small cone: volume of large cone : 1:15a)If the question can be answered with statement I alone but not statement II alone, or can be answered with statement II alone but not statement I alone.b)If the question cannot be answered with statement I alone or with statement II alone, but can be answered if both statements are used together.c)If the question can be answered with either statement alone.d)If the question cannot be answered with the information provided.Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of A right circular cone has height H and radius R. A small cone is cut off at the top by a plane parallel to the base. At what height above the base the section has been made?Statement (I): H = 20 cmStatement (II): Volume of small cone: volume of large cone : 1:15a)If the question can be answered with statement I alone but not statement II alone, or can be answered with statement II alone but not statement I alone.b)If the question cannot be answered with statement I alone or with statement II alone, but can be answered if both statements are used together.c)If the question can be answered with either statement alone.d)If the question cannot be answered with the information provided.Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A right circular cone has height H and radius R. A small cone is cut off at the top by a plane parallel to the base. At what height above the base the section has been made?Statement (I): H = 20 cmStatement (II): Volume of small cone: volume of large cone : 1:15a)If the question can be answered with statement I alone but not statement II alone, or can be answered with statement II alone but not statement I alone.b)If the question cannot be answered with statement I alone or with statement II alone, but can be answered if both statements are used together.c)If the question can be answered with either statement alone.d)If the question cannot be answered with the information provided.Correct 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
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup