$3.$ A storage tank for liquid fuel is designed as a closed cylindrical structure with flat ends, having a total volume of $\backslash (62\mathrm{.}83\backslash$mathrm$\{$~m$\}^\{3\}\backslash ).$ The tank$\text{'}$s radius r and length L is designed to withstand high internal pressure. The surface of the tank is important for evaluating the material strength and pressure resistance. a$.$ Develop an expression for the total surface area of the tank in terms of r $.$ b$.$ Apply the partial differentiation method to determine the dimensions of the tank. c$.$ Identify whether the surface area of the tank is maximum of minimum. $($second derivative$)$ d$.$ If the closed tank is manufactured in a closed surface area, express the r and L that maximize the volume of the tank.