$($a$)$ A steel rod is $3\mathrm{.}000$ cm in diameter at $250$C$.$ A brass ring has an interior diameter of $2\mathrm{.}992$

cm at $250$C$.$ At what common temperature will the ring just slide onto the rod? $($the difference in

expansion between two materials must fill the gap or their final diameters are equal$)($ brass $=19$

x $10-6$ C$-1$ and steel $=11$ x $10-6$ C$-1)($~$3600$C$)$

$($b$)$ At what temperature the gap between the brass ring and the steel rod becomes $0\mathrm{.}0200$ cm$?$

$(12010$C$)$