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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 circumference of two circles are in the ratio 2 : 3 then ratio of their areas is 4 : 9.
Reason : The circumference of a circle of radius r is 2πr and its area is πr2.
- 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 'A'. Can you explain this answer?
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Direction: In the Following Questions, A Statement of Assertion (A) I...
Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
Given,
Now, ratio of their areas be
Also, circumference of circle = 2πr.
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Direction: In the Following Questions, A Statement of Assertion (A) I...
Assertion: If the circumference of two circles are in the ratio 2:3, then the ratio of their areas is 4:9.
Reason: The circumference of a circle of radius r is 2πr and its area is πr².
Explanation:
To understand this assertion and reason, let's consider two circles with radii r₁ and r₂, and their respective circumferences C₁ and C₂, and areas A₁ and A₂.
The circumference of a circle is given by the formula C = 2πr.
So, we can write the given ratio of the circumferences as:
C₁ : C₂ = 2 : 3
Now, let's substitute the formula for circumference in terms of radius:
2πr₁ : 2πr₂ = 2 : 3
Dividing both sides of the equation by 2π:
r₁ : r₂ = 2 : 3
This implies that the ratio of the radii of the two circles is also 2:3.
Now, let's consider the formula for the area of a circle, which is given by A = πr².
The area of the first circle is A₁ = πr₁², and the area of the second circle is A₂ = πr₂².
To find the ratio of the areas, we can write:
A₁ : A₂ = πr₁² : πr₂²
Dividing both sides of the equation by π:
r₁² : r₂² = 2 : 3
Since we know that r₁ : r₂ = 2 : 3, we can square both sides of the equation:
(r₁/r₂)² = (2/3)²
Simplifying, we get:
r₁² : r₂² = 4 : 9
Therefore, the ratio of the areas of the two circles is 4:9, which proves the assertion.
Conclusion:
Both the assertion and reason are true, and the reason is the correct explanation of the assertion. The given explanation shows that if the circumferences of two circles are in the ratio 2:3, then the ratio of their areas will be 4:9.
Reason: The circumference of a circle of radius r is 2πr and its area is πr².
Explanation:
To understand this assertion and reason, let's consider two circles with radii r₁ and r₂, and their respective circumferences C₁ and C₂, and areas A₁ and A₂.
The circumference of a circle is given by the formula C = 2πr.
So, we can write the given ratio of the circumferences as:
C₁ : C₂ = 2 : 3
Now, let's substitute the formula for circumference in terms of radius:
2πr₁ : 2πr₂ = 2 : 3
Dividing both sides of the equation by 2π:
r₁ : r₂ = 2 : 3
This implies that the ratio of the radii of the two circles is also 2:3.
Now, let's consider the formula for the area of a circle, which is given by A = πr².
The area of the first circle is A₁ = πr₁², and the area of the second circle is A₂ = πr₂².
To find the ratio of the areas, we can write:
A₁ : A₂ = πr₁² : πr₂²
Dividing both sides of the equation by π:
r₁² : r₂² = 2 : 3
Since we know that r₁ : r₂ = 2 : 3, we can square both sides of the equation:
(r₁/r₂)² = (2/3)²
Simplifying, we get:
r₁² : r₂² = 4 : 9
Therefore, the ratio of the areas of the two circles is 4:9, which proves the assertion.
Conclusion:
Both the assertion and reason are true, and the reason is the correct explanation of the assertion. The given explanation shows that if the circumferences of two circles are in the ratio 2:3, then the ratio of their areas will be 4:9.
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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 circumference of two circles are in the ratio 2 : 3 then ratio of their areas is 4 : 9.Reason : The circumference of a circle of radius r is 2πr and its area is πr2.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 'A'. Can you explain this answer? for Class 10 2025 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 circumference of two circles are in the ratio 2 : 3 then ratio of their areas is 4 : 9.Reason : The circumference of a circle of radius r is 2πr and its area is πr2.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 'A'. Can you explain this answer? covers all topics & solutions for Class 10 2025 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 circumference of two circles are in the ratio 2 : 3 then ratio of their areas is 4 : 9.Reason : The circumference of a circle of radius r is 2πr and its area is πr2.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 'A'. 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 circumference of two circles are in the ratio 2 : 3 then ratio of their areas is 4 : 9.Reason : The circumference of a circle of radius r is 2πr and its area is πr2.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 'A'. Can you explain this answer? for Class 10 2025 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 circumference of two circles are in the ratio 2 : 3 then ratio of their areas is 4 : 9.Reason : The circumference of a circle of radius r is 2πr and its area is πr2.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 'A'. Can you explain this answer? covers all topics & solutions for Class 10 2025 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 circumference of two circles are in the ratio 2 : 3 then ratio of their areas is 4 : 9.Reason : The circumference of a circle of radius r is 2πr and its area is πr2.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 'A'. 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 circumference of two circles are in the ratio 2 : 3 then ratio of their areas is 4 : 9.Reason : The circumference of a circle of radius r is 2πr and its area is πr2.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 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 10.
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Here you can find the meaning 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 circumference of two circles are in the ratio 2 : 3 then ratio of their areas is 4 : 9.Reason : The circumference of a circle of radius r is 2πr and its area is πr2.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 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation 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 circumference of two circles are in the ratio 2 : 3 then ratio of their areas is 4 : 9.Reason : The circumference of a circle of radius r is 2πr and its area is πr2.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 'A'. 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 circumference of two circles are in the ratio 2 : 3 then ratio of their areas is 4 : 9.Reason : The circumference of a circle of radius r is 2πr and its area is πr2.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 'A'. 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 circumference of two circles are in the ratio 2 : 3 then ratio of their areas is 4 : 9.Reason : The circumference of a circle of radius r is 2πr and its area is πr2.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 'A'. 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 circumference of two circles are in the ratio 2 : 3 then ratio of their areas is 4 : 9.Reason : The circumference of a circle of radius r is 2πr and its area is πr2.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 'A'. Can you explain this answer? tests, examples and also practice Class 10 tests.
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