$10\mathrm{.}12.$ The $10-$year IDF curve for a $10-$ha site in Cleveland, Ohio, is given by

$i=\frac{1209}{(t+8\mathrm{.}86{)}^{0\mathrm{.}79}}$

where $i$ is the average rainfall intensity in $m\frac{m}{h}$ and $t$ is the rainfall duration in minutes. $($a$)$ Determine the peak runoff rate to a drainage structure located in a residential area with single$-$family housing where the catchment area is $0\mathrm{.}5$ ha and the time of concentration is $10$min. $($b$)$ If the available soil storage on the site is $8cm,$ determine the curve number and the volume of runoff $($in $m^3)$ for a $10-$year $24-$h storm.