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 _____________________

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 ___________________

A cylindrical blind riser with diameter $$d$$ and height $$h,$$ is placed on the top of the mold cavity of a closed type sand mold as shown in the figure. If the riser is of constant volume, then the rate of solidification in the riser is the least when the ratio $$h:d$$ is