Heat is removed from a molten metal of mass $$2$$ $$kg$$ at a constant rate of $$10$$ $$kW$$ till it is completely solidified. The cooling curve is shown in the figure.

Assuming uniform temperature throughout the volume of the metal during solidification, the latent heat of fusion of the metal (in $$kJ/kg$$) is ______________

A cylindrical job with diameter of $$200$$ $$mm$$ and height of $$100$$ $$mm$$ is to be cast using modulus method of riser design. Assume that the bottom surface of cylindrical riser does not contribute as cooling surface. If the diameter of the riser is equal to its height, then the height of the riser (in $$mm$$) is

Ratio of solidification time of a cylindrical casting (height $$=$$ radius) to that of a cubic casting of side two times the height of cylindrical casting is ____________

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 _______________