A watershed covering $50$ acres with a runoff coefficient of $0\mathrm{.}4$ and a frequency coefficient of $1\mathrm{.}1$ experiences flooding at the outlet. Time of concentration for this basin is $1$ hour, and the rainfall intensity for various durations is provided in the following table. Our objective is to determine the maximum storage required for designing a detention pond. $(15$ p$)$ Assuming a maximum allowable discharge of $40cfs$ at the pond outlet and a pond depth of $8ft,$ could you calculate the required area for constructing the detention pond? $(5$ p$)$ Additionally, what is the critical duration for this watershed? $(5$ p$)$

$\backslash$table$[[\backslash$table$[[$Storm$],[$Duration$]],\backslash$table$[[$Rainfal$],[$Intensity$],[($in$/$hr$)]],,,],[5$min,$12\mathrm{.}1,,,],[10$min,$8\mathrm{.}86,,,],[15$min,$7\mathrm{.}21,,,],[30$min,$5\mathrm{.}42,,,],[60$min,$3\mathrm{.}68,,,],[2hr,2\mathrm{.}33,,,],[3hr,1\mathrm{.}78,,,],[6hr,1\mathrm{.}13,,,],[12hr,0\mathrm{.}706,,,],[24hr,0\mathrm{.}424,,,]]$

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