Raw data for the isothermal reaction $AB$ is given in the following table.

$\backslash$table$[[x,0,0\mathrm{.}1,0\mathrm{.}2,0\mathrm{.}4,0\mathrm{.}6,0\mathrm{.}7,0\mathrm{.}8],[-r_1(\frac{\text{m}\text{o}\text{l}}{m^3(s)}),0\mathrm{.}360,0\mathrm{.}296,0\mathrm{.}240,0\mathrm{.}156,0\mathrm{.}090,0\mathrm{.}073,0\mathrm{.}040]]$

If the reaction is to be carried out in a CSTR and species A enters the reactor at a molar flow rate of $0\mathrm{.}5mo\frac{l}{s}$ :

$($a$)$ Calculate the reactor volume necessary to achieve $70\%$ conversion.

$($b$)$ Sketch the Levenspiel plot and shade the area that would give the CSTR volume necessary to achieve $70\%$ conversion.