A regular square based pyramid is inscribed in a sphere of given radius `R` so that all vertices of the pyramid belong to the sphere. Find the greatest value of the volume of the pyramid.

Height of greatest cone inscribed in a sphere of radius r is

A cylinder is inscribed in a sphere of radius r What is the radius of the cylinder of maximum volume ?

A prism and a pyramid have the same base and the same height. Find the ratio of the volumes of the prism and the pyramid.

A cube is inscribed in a hemisphere of radius R, such that four of its vertices lie on the base of the hemisphere and the other four touch the hemispherical surface of the half-sphere. What is the volume of the cube?

A regular square pyramid is placed in a cube so that the base of the pyramid and that of the cube coincide. The vertex of the pyramid lies on the face of the cube opposite to the base, as shown. An edge of the cube is 7 inches. How many square inches (approximately) are in the posi- tive difference between the surface area of the cube and the surface area of the pyramid ?

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

A cylinder is inscribed in a sphere of radius R . The volume V of the cylinder is written as v=f(x), wherex is the height of the cylinder

The lateral edge of a regular rectangular pyramid is a cm long.The lateral edge makes an angle alpha with the plane of the base.Find the value of alpha for which the volume of the pyramid is greatest.

Height of a cone,inscribed in a sphere of radius r, having greatest curved surface is

The base of a pyramid is a square whose side is 10 cm. It's slant and vertical heights are 13 and 12 . Then , find the total surface area and volume of the pyramid .