$($a$)$ A circular copper ring at $24\mathrm{.}0$C has a hole with an area of $9\mathrm{.}96$ cm$2.$ What minimum temperature must it have so that it can be slipped onto a steel metal rod having a cross$-$sectional area of $10\mathrm{.}0$ cm$2?$

Your response differs from the correct answer by more than $10\%.$ Double check your calculations.$$C

$($b$)$ Suppose the ring and the rod are heated simultaneously. What change in temperature of both will allow the ring to be slipped onto the end of the rod? $($Assume no significant change in the coefficients of linear expansion over this temperature range.$)$