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

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.

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

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

Find the total surface area of a cone, if its slant height is 21 m and diameter of its base is 24 m.

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

A right circular cylinder has base radius 14 cm and height 21 cm. Find its volume.

The radius of the base of a cone is 14 cm and its height is 15 cm. Find the volume of the cone.

A solid consisting of a right circular conce of height 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of wate such that it touches the bottom. Find the volume of water left in the cylinder. if the radius of the cylinder is 60 cm and its height is 150 cm.

The area of the base of a cylinder is 40 cm^(2) and its height is 10 cm. Find the volume of the cylinder.

Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius R is (2R)/(sqrt(3)) . Also find the maximum volume.