For the case of molding, it is decided to replace a spherical riser of diameter $$100$$ $$mm$$ by a cylindrical riser. Determine size of the cylindrical riser that will have the identical solidification time. Assume blind risering & ratio of height to radius of cylinder is $$2.$$

Match the following

While cooling, a cubical casting of side $$40mm$$ undergoes $$3\% ,\,\,4\% $$ and $$5\% $$ volume shrinkage during the liquid state, phase transition and solid state respectively. The volume of metal compensated from the riser is

A $$200$$ $$mm$$ long down sprue has an area of cross section of $$650$$ $$m{m^2}$$ where the pouring basin meets the down sprue (i.e. at the beginning of the down sprue). A constant head of molten metal is maintaining by the pouring basin. The molten metal flow rate is $$6.5 \times {10^5}\,\,\,m{m^3}/s.$$ considering the end of down sprue to be open to atmosphere and an acceleration due to gravity of $${10^4}mm/{s^2},$$ the area of the down sprue in $$m{m^2}$$ at its end (avoiding aspiration effects) should be