For a given volume of a riser, if the solidification time of the molten metal in riser needs to be quadrupled, the surface area of the riser should be made

A mold having dimensions $$100 \times 90 \times 20$$ (all in $$mm$$) is filled with molten metal througgh a gate with height $$'h'$$ and $$C.S$$ area $$A,$$ the mould filling time is $${t_1}$$. The height is now quadrupled and the cross sectional area is halved. The corresponding filling time is $${t_2}$$. The ratio $${t_2}/{t_1}$$ is

In a sand casting process, a sphere and a cylinder of equal volumes are separately cast from the same molten metal under identical conditions. The height and diameter of the cylinder are equal. The ratio of the solidification time of the sphere to that of the cylinder is

During the filling process of a given sand mould cavity by metal through a horizontal runner of circular $$C.S,$$ the frictional head loss of the molten metal in the runner will increase with the