A casting of $$200\,\,mm\,\, \times \,\,100\,\,mm \times 70\,\,mm$$ size solidifies in ten minutes. Estimate solidification time for a $$200\,\,mm\,\, \times \,\,100\,\,mm \times 10\,\,mm$$ casting under similar conditions?

If the freezing ratio equal to (casting area/casting volume)/(riser area/riser volume) & the volumetric ratio equal to riser volume/casting volume, for a disc casting of $$20cm$$ diameter and $$10$$ $$cm$$ thick are $$1.4$$ and $$0.8$$ respectively. The corresponding values for a square disc of $$20$$ $$cm$$ side and $$10$$ $$cm$$ thick if the same cylindrical riser with a height to diameter ratio of unity is used in both cases.

Molten aluminium was poured in a sand mold and the thickness of solid skin formed after $$20$$ seconds and $$50$$ seconds were fond to be $$3mm$$ and $$4.5mm$$ respectively. What would be the thickness of the solid skin at the end of $$100$$ seconds after pouring?