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

Prove that the volume of the largest cone that can be inscribed in a sphere of radius R is 8/27 of the volume of the sphere.

Find the height of the cylinder of maximum volume that can be inscribed in a sphere of radius a.

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 the right circular cone of least curved surface and given volume has an altitude equal to sqrt2 times the radius of the base.

Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius is (2R)/sqrt3 . Also find the maximum volume.

The length of the longest size rectangel of maximum area that can be inscribed in a semicircle of radius 1, so that 2 vertices lie on the diameter, is a) sqrt2 b)2 c) sqrt3 d) (sqrt2)/(3)

The Given figure represents a cylinder inscribed in a sphere. Figure Find an expression for the volume V of the cylinder .

The Given figure represents a cylinder inscribed in a sphere. Find the volume and radius of the largest cylinder.

Find the ratio of the surface area if the radii of two spheres are in the ratio '2: 3 .' What is the ratio of their volume?