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Show that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius r is 4r/3

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Show that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius r is 4r/3

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A sphere of fixed radius (r) is given.
Let R and h be the radius and the height of the cone respectively.

Hence, it can be seen that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius r is 4r/3.

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