Question - Applications of Derivatives - Maxima and Minima - Second Derivative Test

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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. Also find maximum volume in terms of volume of the sphere

Show that the altitude of a right circular cone of maximum volume that can be inscribed in a sphere of radius r is (4r)/3 . Also, show that the maximum volume of the cone is 8/27  of the volume of the sphere.

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