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Direction: In the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct answer as
Assertion : If diameter of a sphere is decreased by 25%, then its curved surface area is decreased by 43.75%.
Reason : Curved surface area is increased when diameter decreases
- a)Both assertion and reason are true and reason is the correct explanation of assertion.
- b)Both assertion and reason are true but reason is not the correct explanation of assertion.
- c)Assertion is true but reason is false.
- d)Assertion is false but reason is true.
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Direction: In the following questions, a statement of Assertion is gi...
Let the diameter of sphere be 2r.
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Decreased diameter
New diameter = 3r/2
and Radius, r = 3r/4
Curved surface area of sphere = 4πr2
New curved surface area
Curved surface area is decreased by 43.75%.
As if diameter is decreased, curved surface area is decreased.
Most Upvoted Answer
Direction: In the following questions, a statement of Assertion is gi...
Assertion: If diameter of a sphere is decreased by 25%, then its curved surface area is decreased by 43.75%.
Reason: Curved surface area is increased when diameter decreases
Explanation:
To understand the assertion and reason given in the question, let's break it down and analyze it step by step.
Concept of Curved Surface Area:
The curved surface area of a sphere is the total area of its curved surface. It is given by the formula:
Curved Surface Area = 4πr², where r is the radius of the sphere.
Assertion: If diameter of a sphere is decreased by 25%, then its curved surface area is decreased by 43.75%.
The assertion states that if the diameter of a sphere is decreased by 25%, then its curved surface area is decreased by 43.75%.
Reason: Curved surface area is increased when diameter decreases.
The reason states that when the diameter of a sphere decreases, the curved surface area increases.
Analysis:
Let's assume the initial diameter of the sphere is D and the radius is R.
So, the initial curved surface area (CSA) of the sphere can be calculated using the formula: CSA = 4πR².
According to the assertion, if the diameter is decreased by 25%, the new diameter becomes 0.75D.
The new radius of the sphere can be calculated using the formula: Radius = Diameter/2.
So, the new radius is 0.75D/2 = 0.375D.
Now, let's calculate the new curved surface area (CSA') using the formula: CSA' = 4π(0.375D)².
Now, we can compare the initial curved surface area (CSA) and the new curved surface area (CSA').
Calculation:
Initial CSA = 4πR²
New CSA = 4π(0.375D)²
Now, let's calculate the ratio of the new CSA to the initial CSA:
New CSA / Initial CSA = 4π(0.375D)² / 4πR²
= (0.375D)² / R²
= 0.375²
= 0.140625
This calculation shows that the new curved surface area (CSA') is 0.140625 times the initial curved surface area (CSA).
To calculate the percentage decrease in the curved surface area, we can subtract this ratio from 1 and multiply by 100:
Percentage decrease = (1 - New CSA / Initial CSA) x 100
= (1 - 0.140625) x 100
= 0.859375 x 100
= 85.9375%
Conclusion:
From the analysis, we can see that the assertion is true. When the diameter of a sphere is decreased by 25%, the curved surface area is decreased by approximately 85.9375%.
However, the reason given is false. When the diameter decreases, the curved surface area of the sphere decreases, not increases. Hence, the correct answer is option C - Assertion is true but reason is false.
Reason: Curved surface area is increased when diameter decreases
Explanation:
To understand the assertion and reason given in the question, let's break it down and analyze it step by step.
Concept of Curved Surface Area:
The curved surface area of a sphere is the total area of its curved surface. It is given by the formula:
Curved Surface Area = 4πr², where r is the radius of the sphere.
Assertion: If diameter of a sphere is decreased by 25%, then its curved surface area is decreased by 43.75%.
The assertion states that if the diameter of a sphere is decreased by 25%, then its curved surface area is decreased by 43.75%.
Reason: Curved surface area is increased when diameter decreases.
The reason states that when the diameter of a sphere decreases, the curved surface area increases.
Analysis:
Let's assume the initial diameter of the sphere is D and the radius is R.
So, the initial curved surface area (CSA) of the sphere can be calculated using the formula: CSA = 4πR².
According to the assertion, if the diameter is decreased by 25%, the new diameter becomes 0.75D.
The new radius of the sphere can be calculated using the formula: Radius = Diameter/2.
So, the new radius is 0.75D/2 = 0.375D.
Now, let's calculate the new curved surface area (CSA') using the formula: CSA' = 4π(0.375D)².
Now, we can compare the initial curved surface area (CSA) and the new curved surface area (CSA').
Calculation:
Initial CSA = 4πR²
New CSA = 4π(0.375D)²
Now, let's calculate the ratio of the new CSA to the initial CSA:
New CSA / Initial CSA = 4π(0.375D)² / 4πR²
= (0.375D)² / R²
= 0.375²
= 0.140625
This calculation shows that the new curved surface area (CSA') is 0.140625 times the initial curved surface area (CSA).
To calculate the percentage decrease in the curved surface area, we can subtract this ratio from 1 and multiply by 100:
Percentage decrease = (1 - New CSA / Initial CSA) x 100
= (1 - 0.140625) x 100
= 0.859375 x 100
= 85.9375%
Conclusion:
From the analysis, we can see that the assertion is true. When the diameter of a sphere is decreased by 25%, the curved surface area is decreased by approximately 85.9375%.
However, the reason given is false. When the diameter decreases, the curved surface area of the sphere decreases, not increases. Hence, the correct answer is option C - Assertion is true but reason is false.
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Direction: In the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct answer asAssertion : If diameter of a sphere is decreased by 25%, then its curved surface area is decreased by 43.75%.Reason : Curved surface area is increased when diameter decreasesa)Both assertion and reason are true and reason is the correct explanation of assertion.b)Both assertion and reason are true but reason is not the correct explanation of assertion.c)Assertion is true but reason is false.d)Assertion is false but reason is true.Correct answer is option 'C'. Can you explain this answer?
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Direction: In the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct answer asAssertion : If diameter of a sphere is decreased by 25%, then its curved surface area is decreased by 43.75%.Reason : Curved surface area is increased when diameter decreasesa)Both assertion and reason are true and reason is the correct explanation of assertion.b)Both assertion and reason are true but reason is not the correct explanation of assertion.c)Assertion is true but reason is false.d)Assertion is false but reason is true.Correct answer is option 'C'. Can you explain this answer? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Direction: In the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct answer asAssertion : If diameter of a sphere is decreased by 25%, then its curved surface area is decreased by 43.75%.Reason : Curved surface area is increased when diameter decreasesa)Both assertion and reason are true and reason is the correct explanation of assertion.b)Both assertion and reason are true but reason is not the correct explanation of assertion.c)Assertion is true but reason is false.d)Assertion is false but reason is true.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction: In the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct answer asAssertion : If diameter of a sphere is decreased by 25%, then its curved surface area is decreased by 43.75%.Reason : Curved surface area is increased when diameter decreasesa)Both assertion and reason are true and reason is the correct explanation of assertion.b)Both assertion and reason are true but reason is not the correct explanation of assertion.c)Assertion is true but reason is false.d)Assertion is false but reason is true.Correct answer is option 'C'. Can you explain this answer?.
Direction: In the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct answer asAssertion : If diameter of a sphere is decreased by 25%, then its curved surface area is decreased by 43.75%.Reason : Curved surface area is increased when diameter decreasesa)Both assertion and reason are true and reason is the correct explanation of assertion.b)Both assertion and reason are true but reason is not the correct explanation of assertion.c)Assertion is true but reason is false.d)Assertion is false but reason is true.Correct answer is option 'C'. Can you explain this answer? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Direction: In the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct answer asAssertion : If diameter of a sphere is decreased by 25%, then its curved surface area is decreased by 43.75%.Reason : Curved surface area is increased when diameter decreasesa)Both assertion and reason are true and reason is the correct explanation of assertion.b)Both assertion and reason are true but reason is not the correct explanation of assertion.c)Assertion is true but reason is false.d)Assertion is false but reason is true.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction: In the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct answer asAssertion : If diameter of a sphere is decreased by 25%, then its curved surface area is decreased by 43.75%.Reason : Curved surface area is increased when diameter decreasesa)Both assertion and reason are true and reason is the correct explanation of assertion.b)Both assertion and reason are true but reason is not the correct explanation of assertion.c)Assertion is true but reason is false.d)Assertion is false but reason is true.Correct answer is option 'C'. Can you explain this answer?.
Solutions for Direction: In the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct answer asAssertion : If diameter of a sphere is decreased by 25%, then its curved surface area is decreased by 43.75%.Reason : Curved surface area is increased when diameter decreasesa)Both assertion and reason are true and reason is the correct explanation of assertion.b)Both assertion and reason are true but reason is not the correct explanation of assertion.c)Assertion is true but reason is false.d)Assertion is false but reason is true.Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 9.
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