Two castings, a cube and a slab of the same material solidify under identical conditions. The volumes of the castings are equal but the slab dimensions are in the ratio of $$1:2:4$$, find the ratio of the solidification times of the cube to that of the slab.

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.