If a cone of maximum volume is inscribed in a given sphere, then the ratio of the height of the cone to the diameter of the sphere is `3//4` (b) `1//3` (c) `1//4` (d) `2//3`

The height of the cone of maximum volume inscribed in a sphere of radius R is

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 ratio between the height of a right circular cone of maximum volume inscribed in given sphere and the diameter of the sphere is

A sphere of maximum volume is cut out from a solid hemisphere of radius r. The ratio of the volume of the hemisphere to that of the cut out sphere is: (a) 3:2 (b) 4:1 (c) 4:3 (d) 7:4

The radius of a sphere is equal to the radius of the base of a right circular cone,and the volume of the sphere is double the volume of the cone.The ratio of the height of the cone to the radius of its base is (a) 2:1quad (b) 1:2 (c) 2:3quad (d) 3:2

Show that the cone of greatest volume which can be inscribed in a given sphere is such that three times its altitude is twice the diameter of the sphere. Find the volume of the largest come inscribed ina sphere of radius R.