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If a right circular cone, having maximum volume, is inscribed in a sphere of radius 3 cm, then the curved surface area (in cm2) of this cone is:
- a)8√2 π
- b)6√2 π
- c)6√3 π
- d)8√3 π
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
If a right circular cone, having maximum volume, is inscribed in a sph...
(h − R)2 + r2 = R2
r2 = R2 − (h − R)2
R = 3
r2 = q − (h − 3)2
h(−3h + 12) = 0
3h = 12, h = 0
h = 4. r = 2√2.
CSA = πrl
= π × 2√2 × √24
= π 2 × √48 = 8π√3
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If a right circular cone, having maximum volume, is inscribed in a sph...
Given Information:
- The sphere has a radius of 3 cm.
Approach:
- To maximize the volume of the cone inscribed in the sphere, we need to find the height and radius of the cone.
- The curved surface area of the cone can be calculated using the formula: CSA = πr√(r^2 + h^2), where r is the radius and h is the height of the cone.
Finding the dimensions of the cone:
- Let the radius and height of the cone be r and h, respectively.
- The cone is inscribed in the sphere, so the diameter of the sphere is equal to the diagonal of the cone's base, i.e., 2r = 6 cm.
- Since the volume of the cone is maximum when it is inscribed in a sphere, the cone is a right circular cone.
- Using the Pythagorean theorem, we have r^2 + h^2 = 9.
Maximizing the volume of the cone:
- The volume of the cone is given by V = (1/3)πr^2h.
- Substituting 2r = 6 into r^2 + h^2 = 9, we get r = 3 and h = √6.
- Therefore, the maximum volume of the cone is V = π(3)(√6) = 3√6π.
Calculating the curved surface area of the cone:
- Substituting r = 3 and h = √6 into the formula for the curved surface area, we get CSA = π(3)√(3^2 + (√6)^2) = 8√3π.
Conclusion:
- The curved surface area of the cone is 8√3π cm^2, which corresponds to option 'D'.
- The sphere has a radius of 3 cm.
Approach:
- To maximize the volume of the cone inscribed in the sphere, we need to find the height and radius of the cone.
- The curved surface area of the cone can be calculated using the formula: CSA = πr√(r^2 + h^2), where r is the radius and h is the height of the cone.
Finding the dimensions of the cone:
- Let the radius and height of the cone be r and h, respectively.
- The cone is inscribed in the sphere, so the diameter of the sphere is equal to the diagonal of the cone's base, i.e., 2r = 6 cm.
- Since the volume of the cone is maximum when it is inscribed in a sphere, the cone is a right circular cone.
- Using the Pythagorean theorem, we have r^2 + h^2 = 9.
Maximizing the volume of the cone:
- The volume of the cone is given by V = (1/3)πr^2h.
- Substituting 2r = 6 into r^2 + h^2 = 9, we get r = 3 and h = √6.
- Therefore, the maximum volume of the cone is V = π(3)(√6) = 3√6π.
Calculating the curved surface area of the cone:
- Substituting r = 3 and h = √6 into the formula for the curved surface area, we get CSA = π(3)√(3^2 + (√6)^2) = 8√3π.
Conclusion:
- The curved surface area of the cone is 8√3π cm^2, which corresponds to option 'D'.
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If a right circular cone, having maximum volume, is inscribed in a sphere of radius 3 cm, then the curved surface area (in cm2) of this cone is: a)8√2 πb)6√2 πc)6√3 πd)8√3 πCorrect answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If a right circular cone, having maximum volume, is inscribed in a sphere of radius 3 cm, then the curved surface area (in cm2) of this cone is: a)8√2 πb)6√2 πc)6√3 πd)8√3 πCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a right circular cone, having maximum volume, is inscribed in a sphere of radius 3 cm, then the curved surface area (in cm2) of this cone is: a)8√2 πb)6√2 πc)6√3 πd)8√3 πCorrect answer is option 'D'. Can you explain this answer?.
If a right circular cone, having maximum volume, is inscribed in a sphere of radius 3 cm, then the curved surface area (in cm2) of this cone is: a)8√2 πb)6√2 πc)6√3 πd)8√3 πCorrect answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If a right circular cone, having maximum volume, is inscribed in a sphere of radius 3 cm, then the curved surface area (in cm2) of this cone is: a)8√2 πb)6√2 πc)6√3 πd)8√3 πCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a right circular cone, having maximum volume, is inscribed in a sphere of radius 3 cm, then the curved surface area (in cm2) of this cone is: a)8√2 πb)6√2 πc)6√3 πd)8√3 πCorrect answer is option 'D'. Can you explain this answer?.
Solutions for If a right circular cone, having maximum volume, is inscribed in a sphere of radius 3 cm, then the curved surface area (in cm2) of this cone is: a)8√2 πb)6√2 πc)6√3 πd)8√3 πCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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If a right circular cone, having maximum volume, is inscribed in a sphere of radius 3 cm, then the curved surface area (in cm2) of this cone is: a)8√2 πb)6√2 πc)6√3 πd)8√3 πCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for If a right circular cone, having maximum volume, is inscribed in a sphere of radius 3 cm, then the curved surface area (in cm2) of this cone is: a)8√2 πb)6√2 πc)6√3 πd)8√3 πCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of If a right circular cone, having maximum volume, is inscribed in a sphere of radius 3 cm, then the curved surface area (in cm2) of this cone is: a)8√2 πb)6√2 πc)6√3 πd)8√3 πCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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