Three castings are of the same material, volume and cast under similar conditions. One is a sphere, another is a cube and the third is cylinder with its length being equal to its diameter.

The ratio of solidification times of sphere to the cube is

A rectangular block of steel $$C.S$$ $$100\,\, \times \,\,150mm$$ and $$250mm$$ height is to be cast with out any riser. The block is moulded entirely in the drag of a green sand flask & is tap gated. The cope of the flask is $$200mm$$ height & the height of the metal during pouring is $$100mm$$ above the cope level. A tapered sprue is employed & the gating ratio is $$1:4:2$$. Assume no energy losses in the system. The time taken (in seconds) to fill the casting cavity, if the tapered sprues with $$500$$ $$m{m^2}$$ exit area is used.

A steel plate $$40cm \times 30cm \times 0.3cm$$ is to be cast. The volume shrinkage of steel during solidification is $$3\% .$$ A cylindrical side riser with diameter $$4cm$$ and height $$4cm$$ is used. The riser volume should at least be $$3$$ times that the dictated by shrinkage consideration. Is the riser volume sufficient if not what is the riser size?