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The ratio of the altitude of the cone of greatest volume which can be inscribed in a given sphere to the diameter of the sphere is
  • a)
    2/3
  • b)
    3/4
  • c)
    1/3
  • d)
    1/4
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The ratio of the altitude of the cone of greatest volume which can be ...
Explanation:

Volume of cone inscribed in sphere:
- Let the radius of the sphere be 'r'.
- The radius of the base of the inscribed cone will also be 'r'.
- Let the altitude of the cone be 'h'.
- The volume of a cone is given by V = (1/3)πr²h.

Relation between dimensions of cone and sphere:
- The altitude of the cone will be equal to the diameter of the sphere in order to maximize the volume of the cone.
- So, h = 2r.

Ratio of altitude to diameter:
- Ratio of altitude to diameter = h / 2r = 2r / 2r = 2 / 2 = 2/3.
Therefore, the ratio of the altitude of the cone of greatest volume which can be inscribed in a given sphere to the diameter of the sphere is 2/3. Hence, the correct answer is option 'A'.
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The ratio of the altitude of the cone of greatest volume which can be inscribed in a given sphere to the diameter of the sphere isa)2/3b)3/4c)1/3d)1/4Correct answer is option 'A'. Can you explain this answer?
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