Show that semi-vertical angle of right circular cone of given surface area and maximum volume is `sin^(-1)(1/3)`.

show that the semi vertical angle of a right circular cone of given total surface area and max volume is sin ^(-1)((1)/(3))

Volume of a Right Circular Cone

Prove that the semi-vertical angle of the right circular cone of given volume and least curved surface is cot^(-1)(sqrt(2))

Show that the right circular cylinder,open at the top,and of given surface area and maximum volume is such that its height is equal to the radius of the base.

Show that the height of a closed right circular cylinder of given surface and maximum volume,is equal to the diameter of its base.

Show that the semi - vertical angle of the right - circular cone of maximum volume and of given slant height is : (i) tan^(-1)sqrt2 (ii) cos^(-1)""(1)/(sqrt3).

Total Surface Area of A Right Circular cone

Volume of frustum of right circular cone

Show that the semi-vertical angle of the cone of the maximum volume and of given slant height is tan^(-1)sqrt(2)