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 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.

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

What is the radius of the largest sphere that can be carved from a cube of edge 12 centimetres?

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

What is the surface area of the largest sphere that can be carved out from a cube of side 8 centimetres?

The radius and height of a cone are 12 centimetres, and 6 centimetres respectively. a) What is its volume? b) If this cone is, cut parallel to its base, along the midpoint of its height,what is. the radiús of the small cone obtained? c) What is the volume of the small cone? d) Find the ratio of the volumes of the small cone and the first cone.