Silicon rods are produced in a process in which a rotating cylinder of Si is slowly drawn from a heated bath. If the initial bath contains $62$ kg Si$,$ and a cylinder $17\mathrm{.}5$ cm in diameter is to be removed slowly from the melt at the rate of $3$ mm per min, how long will it take to remove onehalf of the Si$?$ What is the accumulation of Si in the melt?