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 ____________

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 _____________________

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 _____________________

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 ___________________