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DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion : If the radius of a cone is halved and volume is not changed, then height remains same.
Reason : If the radius of a cone is halved and volume is not changed then height must become four times of the original height.
- a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
- b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
- c)Assertion (A) is true but reason (R) is false.
- d)Assertion (A) is false but reason (R) is true.
Correct answer is option 'D'. Can you explain this answer?
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DIRECTION : In the following questions, a statement of assertion (A) ...
Assertion: If the radius of a cone is halved and volume is not changed, then the height remains the same.
Reason: If the radius of a cone is halved and volume is not changed, then the height must become four times the original height.
Explanation:
To understand this assertion and reason, let's consider the formula for the volume of a cone:
Volume of a cone = (1/3) * π * r^2 * h
Where,
r = radius of the cone
h = height of the cone
Assertion Explanation:
When the radius of a cone is halved, let's say the new radius is r/2, and the volume is not changed, it means the original volume and the new volume are the same.
Original Volume = (1/3) * π * r^2 * h
New Volume = (1/3) * π * (r/2)^2 * h
Since the volume is not changed, we can equate the original volume and the new volume:
(1/3) * π * r^2 * h = (1/3) * π * (r/2)^2 * h
Simplifying the equation:
r^2 = (r/2)^2
This equation is true only when r = 0. Hence, the radius cannot be halved without changing the volume of the cone. Therefore, the assertion is false.
Reason Explanation:
The reason given states that if the radius of a cone is halved and the volume is not changed, then the height must become four times the original height.
Let's assume the original height of the cone is h. If the radius is halved, the new radius becomes r/2. According to the reason, the new height should be four times the original height, which is 4h.
However, as explained in the assertion, when the radius is halved, the volume cannot remain the same. Therefore, the reason is not valid.
Hence, both the assertion and the reason are false.
Therefore, the correct answer is option 'd' - Assertion (A) is false, but reason (R) is true.
Reason: If the radius of a cone is halved and volume is not changed, then the height must become four times the original height.
Explanation:
To understand this assertion and reason, let's consider the formula for the volume of a cone:
Volume of a cone = (1/3) * π * r^2 * h
Where,
r = radius of the cone
h = height of the cone
Assertion Explanation:
When the radius of a cone is halved, let's say the new radius is r/2, and the volume is not changed, it means the original volume and the new volume are the same.
Original Volume = (1/3) * π * r^2 * h
New Volume = (1/3) * π * (r/2)^2 * h
Since the volume is not changed, we can equate the original volume and the new volume:
(1/3) * π * r^2 * h = (1/3) * π * (r/2)^2 * h
Simplifying the equation:
r^2 = (r/2)^2
This equation is true only when r = 0. Hence, the radius cannot be halved without changing the volume of the cone. Therefore, the assertion is false.
Reason Explanation:
The reason given states that if the radius of a cone is halved and the volume is not changed, then the height must become four times the original height.
Let's assume the original height of the cone is h. If the radius is halved, the new radius becomes r/2. According to the reason, the new height should be four times the original height, which is 4h.
However, as explained in the assertion, when the radius is halved, the volume cannot remain the same. Therefore, the reason is not valid.
Hence, both the assertion and the reason are false.
Therefore, the correct answer is option 'd' - Assertion (A) is false, but reason (R) is true.
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DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : If the radius of a cone is halved and volume is not changed, then height remains same.Reason : If the radius of a cone is halved and volume is not changed then height must become four times of the original height.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'D'. Can you explain this answer?
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DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : If the radius of a cone is halved and volume is not changed, then height remains same.Reason : If the radius of a cone is halved and volume is not changed then height must become four times of the original height.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'D'. 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 DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : If the radius of a cone is halved and volume is not changed, then height remains same.Reason : If the radius of a cone is halved and volume is not changed then height must become four times of the original height.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'D'. 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 DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : If the radius of a cone is halved and volume is not changed, then height remains same.Reason : If the radius of a cone is halved and volume is not changed then height must become four times of the original height.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'D'. Can you explain this answer?.
DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : If the radius of a cone is halved and volume is not changed, then height remains same.Reason : If the radius of a cone is halved and volume is not changed then height must become four times of the original height.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'D'. 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 DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : If the radius of a cone is halved and volume is not changed, then height remains same.Reason : If the radius of a cone is halved and volume is not changed then height must become four times of the original height.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'D'. 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 DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : If the radius of a cone is halved and volume is not changed, then height remains same.Reason : If the radius of a cone is halved and volume is not changed then height must become four times of the original height.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'D'. Can you explain this answer?.
Solutions for DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : If the radius of a cone is halved and volume is not changed, then height remains same.Reason : If the radius of a cone is halved and volume is not changed then height must become four times of the original height.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 10.
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DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : If the radius of a cone is halved and volume is not changed, then height remains same.Reason : If the radius of a cone is halved and volume is not changed then height must become four times of the original height.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'D'. Can you explain this answer?, a detailed solution for DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : If the radius of a cone is halved and volume is not changed, then height remains same.Reason : If the radius of a cone is halved and volume is not changed then height must become four times of the original height.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : If the radius of a cone is halved and volume is not changed, then height remains same.Reason : If the radius of a cone is halved and volume is not changed then height must become four times of the original height.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : If the radius of a cone is halved and volume is not changed, then height remains same.Reason : If the radius of a cone is halved and volume is not changed then height must become four times of the original height.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice Class 10 tests.
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