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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 : An edge of a cube measures r cm. If the largest possible right circular cone is cut out of this cube, then the volume of the cone is 1/3 πr3.
Reason : Volume of the cone is given by 1/3 πr2h, where r is the radius of the base and h is the height of the cone.
  • 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 'D'. Can you explain this answer?
Verified Answer
Direction: In the following questions, a statement of Assertion is gi...
Height of the cone = r cm.
Diameter of the base = r cm.
Therefore, volume of the cone = 1/3 π(r/2)2.r
= 1/12 πr3
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Most Upvoted Answer
Direction: In the following questions, a statement of Assertion is gi...
Assertion: An edge of a cube measures r cm. If the largest possible right circular cone is cut out of this cube, then the volume of the cone is 1/3 πr3.

Reason: Volume of the cone is given by 1/3 πr2h, where r is the radius of the base and h is the height of the cone.

Explanation:
To understand why the correct answer is option 'D', let's analyze the assertion and reason separately.

Assertion: An edge of a cube measures r cm. If the largest possible right circular cone is cut out of this cube, then the volume of the cone is 1/3 πr3.

When an edge of a cube measures r cm, it means that all sides of the cube are equal and measure r cm. If we cut out the largest possible right circular cone from this cube, the base of the cone will have the same diameter as the edge of the cube, which is r cm. Therefore, the radius of the base of the cone will be r/2 cm.

Now, let's move on to the reason.

Reason: Volume of the cone is given by 1/3 πr2h, where r is the radius of the base and h is the height of the cone.

The formula for the volume of a cone is V = (1/3)πr^2h, where r is the radius of the base and h is the height of the cone. However, in this case, the radius of the base is not r, but r/2 because the base of the cone is half the diameter of the cube's edge. Therefore, we cannot use the given formula to calculate the volume of the cone in this scenario.

Conclusion:
From the analysis above, it is clear that the assertion is false because the radius of the base of the cone is not r, but r/2. However, the reason is true because it states the correct formula for the volume of a cone. Therefore, the correct answer is option 'D' - Assertion is false but the reason is true.
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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 : An edge of a cube measures r cm. If the largest possible right circular cone is cut out of this cube, then the volume of the cone is 1/3 πr3.Reason : Volume of the cone is given by 1/3 πr2h, where r is the radius of the base and h is the height of the cone.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 'D'. 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 : An edge of a cube measures r cm. If the largest possible right circular cone is cut out of this cube, then the volume of the cone is 1/3 πr3.Reason : Volume of the cone is given by 1/3 πr2h, where r is the radius of the base and h is the height of the cone.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 'D'. 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 : An edge of a cube measures r cm. If the largest possible right circular cone is cut out of this cube, then the volume of the cone is 1/3 πr3.Reason : Volume of the cone is given by 1/3 πr2h, where r is the radius of the base and h is the height of the cone.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 'D'. 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 : An edge of a cube measures r cm. If the largest possible right circular cone is cut out of this cube, then the volume of the cone is 1/3 πr3.Reason : Volume of the cone is given by 1/3 πr2h, where r is the radius of the base and h is the height of the cone.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 'D'. Can you explain this answer?.
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