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

Ratio of solidification time of a cylindrical casting (height $$=$$ radius) to that of a cubic casting of side two times the height of cylindrical casting is ____________

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 _______________

An aluminium alloy (density $$2600$$ $$kg/{m^3}$$ ) casting is to be produced. A cylindrical hole of $$100$$ $$mm$$ diameter and $$100$$ $$mm$$ length is made in the casting using sand core (density $$1600$$ $$kg/{m^3}$$ ). The net buoyancy force (in Newton) acting on the core is _____________________