Two castings of the same metal have the same surface area one casting is in the form of a sphere and the other is a cube. What is the ratio of the solidification time for the sphere to that of cube.

Calculate the ratio of the solidification times of two steel cylindrical risers of sizes $$30cm$$ diameter by $$60$$ $$cm$$ in height and $$60cm$$ diameter by $$30$$ $$cm$$ in height subjected to identical conditions of cooling

A down sprue of $$180mm$$ length has diameter of $$20mm$$ at its top end. The liquid metal in the pouring cup is main-tained upto $$60$$ $$mm$$ height. What should be the theoretical diameter of down sprue at its lowest end to ensure that there is no aspiration effects.