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A cone of maximum volume is inscribed in a given sphere. Then prove that ratio of the height of the…

Mathematics20256 marksDerivation
A cone of maximum volume is inscribed in a given sphere. Then prove that ratio of the height of the cone to the diameter of the sphere is equal to $\frac{2}{3}$. [Application]

To show: \text{Ratio of height of cone to diameter of sphere} = \frac{2}{3}

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Applications of Derivatives

From ISC 2025 Specimen Mathematics Paper 1, question 13(i).