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Show that the semi–vertical angle of the right circular cone of given total surface area and maximum volume is sin^-1 1/3.

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Show that the semi–vertical angle of the right circular cone of given total surface area and maximum volume is sin-1 1/3.

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Let r be the radius, l be the slant height and h be the vertical height of a cone of semi-vertical angle α.

Thus V is maximum, when semi vertical angle is sin-1(1/3)

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