The radii of the internal and external surfaces of a metallic spherical shell are 3 cm and 5 cm respectively. It is melted and recast into a solid right circular cone of height 32 cm. Find the diameter of the base of the cone.

Total volume of three identical cones is the same as that of a bigger cone whose height is 9 cm and diameter 40 cm. Find the radius of the base of each smaller cone, if height of each is 108 cm.

A hemispherical bowl of internal radius 9 cm is full of liquid. This liquid is to be filled into conical shaped small containers each of diameter 3 cm and height 4 cm. How many containers are necessary to empty the bowl?

The total area of a solid metallic sphere is 1256 cm³. It is melted and recast into solid right circular cones of radius 2.5 cm and height 8 cm. Calculate :

(i) the radius of the solid sphere,

(ii) the number of cones recast.

[Take π = 3.14]