Prove that the radius of the right circular cylinder of greatest curved surface which can be inscribed in a given cone is half that of the cone.

Prove that the radius of the right circular cylinder of greatest curved surface area which can be inscribed in a given cone is half of that of the cone.

Show that height of the cylinder of greatest volume which can be inscribed in a right circular cone of height h and semi vertical angle alpha is one-third that of the cone and the greatest volume of cylinder is 4/(27)pih^3tan^2alphadot

Show that the cone of the greatest volume which can be inscribed in a given sphere has an altitude equal to 2/3 of the diameter of the sphere.

The base of a right circular cone may not be circular.

Show that the right circular cone of least curved surface and given volume has an altitude equal to sqrt(2) time the radius of the base.

Find the cylinder of maximum volume which can be inscribed in a cone of height h and semivertical angle alpha .

The base radius of a right circular cylinder and a cone are equal and the ratio of their volume is 3:2. Prove that the height of the cone is twice the height of the cylinder.

The diameter of the base of a right circular cone is 6 cm and height is 4 cm . Then the curved surface area of the cone is

The ratio of the lengths of the radii of the bases of a right circular cylinder and of a right circular cone is 3:4 and the ratio of their heights is 2:3 , Find the ratio of the volumes of the cylinder and the cone.

The ratio of the radius of the base of a right circular cone and its height is 3:7 , The volume of the cone is 528c c . Fin the diameter of the cone.