Silicon rods used in the manufacture of chips can be prepared by the Czochralski process in which a cylinder

of rotating silicon is slowly drawn from a heated bath $($see the image below$).30$ kg of silicon in the initial bath

is completely consumed when cylindrical ingot is to be removed slowly from the melt at the rate of $3$ mm$/$min$.$

Calculate the diameter of silicon ingot in cm$.$ Assume that the silicon ingot has a specific gravity of $2\mathrm{.}33.$

$(15$points$)$