The dimensions of a cylindrical side riser (height $$=$$ diameter) for a
$$25cm \times 15cm \times 5cm$$ steel casting are to be determined. For the tabulated shape factor values given below, the diameter of the riser (in $$cm$$) is _______________

A cube and a sphere made of cast iron (each of volume $$1000\,\,c{m^3}$$) were cast under identical conditions. The time taken for solidifying the cube was $$4$$ $$s.$$ The solidification time (in $$s$$) for the sphere is _____________________

The solidification time of a casting is proportional to $${\left( {{V \over A}} \right)^2},$$ Where $$V$$ is the volume of the casting and $$A$$ is the total casting surface area losing heat. Two cubes of same material and size are cast using sand casting process. The top face of one of the cubes is completely insulated. The ratio of the solidification time for the cube with top face insulated to that of the other cube is

A cylindrical riser of $$6$$ $$cm$$ diameter and $$6$$ $$cm$$ height has to be designed for a sand casting mould for producing a steel rectangular plate casting of $$7cm \times 10cm \times 2cm$$ dimensions having the total solidification time of $$1.36$$ minute. The total solidification time (in minute) of the riser is ___________________