Hydrologic mass balance $(15$ points$)$: Use a hydrologic mass balance to solve the following:

a$.(10)$ A lake is approximately $15km$ in length by $5km$ in width. The inflow for the month of August is $3\mathrm{.}5\frac{m^3}{s}$ and the outflow is $2\mathrm{.}15\frac{m^3}{s}.$ The total monthly precipitation is $20\mathrm{.}5cm$ and the evaporation is $8\mathrm{.}2cm.$ The seepage $($infiltration$)$ is estimated to be $1\mathrm{.}35cm.$ Estimate the change in storage $($in $m^3)$ during the month of August.

b$.(5)$ Assume that you want to use this lake as a water supply source and you can control the outflow in the lake. Under the same conditions $($i$.$e$.,$ same inflow, precipitation, infiltration, and evaporation$),$ how much water can you extract in August $($volume$)$ while maintaining steady state conditions in the lake?