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Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
Assertion (A): The Volume and Surface Area of a sphere are related to each other by radius.
Reason (R): Relation between Surface Area S and Volume V is S3 = 36πV2.
- a)Both A and R are true and R is the correct explanation of A.
- b)Both A and R are true and R is not correct explanation of A.
- c)A is true but R is false.
- d)A is false but R is true.
Correct answer is option 'A'. Can you explain this answer?
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Directions : In the following questions, A statement of Assertion (A)...
Volume of sphere = 
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⇒ 
⇒ 
⇒ 
Also, S = 4πr2
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which proves that assertion is correct.
which proves that assertion is correct.Therefore, Both A and R are true and R is the correct explanation for A.
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Directions : In the following questions, A statement of Assertion (A)...
Assertion (A): The Volume and Surface Area of a sphere are related to each other by radius.
Reason (R): The relation between Surface Area S and Volume V is S^3 = 36πV^2.
The correct answer is option 'A' - Both A and R are true and R is the correct explanation of A.
Explanation:
Surface Area of a Sphere:
The surface area of a sphere is given by the formula S = 4πr^2, where S is the surface area and r is the radius of the sphere.
Volume of a Sphere:
The volume of a sphere is given by the formula V = (4/3)πr^3, where V is the volume and r is the radius of the sphere.
Relation between Surface Area and Volume:
To find the relation between the surface area and volume of a sphere, we can equate the surface area formula with the volume formula and solve for one of the variables.
S = 4πr^2
V = (4/3)πr^3
If we solve the surface area formula for r^2 and substitute it into the volume formula, we get:
r^2 = S / (4π)
V = (4/3)πr^3
V = (4/3)π(S / (4π))^3
V = (4/3)π(S^3 / (4^3π^3))
V = (1/3)(S^3 / (π^2))
V = (S^3 / (3π^2))
Therefore, the correct relation between the surface area S and volume V of a sphere is V = (S^3 / (3π^2)).
Comparing this with the given relation S^3 = 36πV^2, we can see that they are equivalent.
Hence, both the assertion and reason are true, and the reason correctly explains the assertion.
Reason (R): The relation between Surface Area S and Volume V is S^3 = 36πV^2.
The correct answer is option 'A' - Both A and R are true and R is the correct explanation of A.
Explanation:
Surface Area of a Sphere:
The surface area of a sphere is given by the formula S = 4πr^2, where S is the surface area and r is the radius of the sphere.
Volume of a Sphere:
The volume of a sphere is given by the formula V = (4/3)πr^3, where V is the volume and r is the radius of the sphere.
Relation between Surface Area and Volume:
To find the relation between the surface area and volume of a sphere, we can equate the surface area formula with the volume formula and solve for one of the variables.
S = 4πr^2
V = (4/3)πr^3
If we solve the surface area formula for r^2 and substitute it into the volume formula, we get:
r^2 = S / (4π)
V = (4/3)πr^3
V = (4/3)π(S / (4π))^3
V = (4/3)π(S^3 / (4^3π^3))
V = (1/3)(S^3 / (π^2))
V = (S^3 / (3π^2))
Therefore, the correct relation between the surface area S and volume V of a sphere is V = (S^3 / (3π^2)).
Comparing this with the given relation S^3 = 36πV^2, we can see that they are equivalent.
Hence, both the assertion and reason are true, and the reason correctly explains the assertion.
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Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): The Volume and Surface Area of a sphere are related to each other by radius.Reason (R): Relation between Surface Area S and Volume V is S3 = 36πV2.a)Both A and R are true and R is the correct explanation of A.b)Both A and R are true and R is not correct explanation of A.c)A is true but R is false.d)A is false but R is true.Correct answer is option 'A'. Can you explain this answer?
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Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): The Volume and Surface Area of a sphere are related to each other by radius.Reason (R): Relation between Surface Area S and Volume V is S3 = 36πV2.a)Both A and R are true and R is the correct explanation of A.b)Both A and R are true and R is not correct explanation of A.c)A is true but R is false.d)A is false but R is true.Correct answer is option 'A'. 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 Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): The Volume and Surface Area of a sphere are related to each other by radius.Reason (R): Relation between Surface Area S and Volume V is S3 = 36πV2.a)Both A and R are true and R is the correct explanation of A.b)Both A and R are true and R is not correct explanation of A.c)A is true but R is false.d)A is false but R is true.Correct answer is option 'A'. 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 Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): The Volume and Surface Area of a sphere are related to each other by radius.Reason (R): Relation between Surface Area S and Volume V is S3 = 36πV2.a)Both A and R are true and R is the correct explanation of A.b)Both A and R are true and R is not correct explanation of A.c)A is true but R is false.d)A is false but R is true.Correct answer is option 'A'. Can you explain this answer?.
Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): The Volume and Surface Area of a sphere are related to each other by radius.Reason (R): Relation between Surface Area S and Volume V is S3 = 36πV2.a)Both A and R are true and R is the correct explanation of A.b)Both A and R are true and R is not correct explanation of A.c)A is true but R is false.d)A is false but R is true.Correct answer is option 'A'. 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 Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): The Volume and Surface Area of a sphere are related to each other by radius.Reason (R): Relation between Surface Area S and Volume V is S3 = 36πV2.a)Both A and R are true and R is the correct explanation of A.b)Both A and R are true and R is not correct explanation of A.c)A is true but R is false.d)A is false but R is true.Correct answer is option 'A'. 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 Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): The Volume and Surface Area of a sphere are related to each other by radius.Reason (R): Relation between Surface Area S and Volume V is S3 = 36πV2.a)Both A and R are true and R is the correct explanation of A.b)Both A and R are true and R is not correct explanation of A.c)A is true but R is false.d)A is false but R is true.Correct answer is option 'A'. Can you explain this answer?.
Solutions for Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): The Volume and Surface Area of a sphere are related to each other by radius.Reason (R): Relation between Surface Area S and Volume V is S3 = 36πV2.a)Both A and R are true and R is the correct explanation of A.b)Both A and R are true and R is not correct explanation of A.c)A is true but R is false.d)A is false but 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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