The column load is $220$ kips $,$ and the thickness of the footing is to be $20$ in $.$ The cohesion of the soil is $500$ psf angle of internal friction of $20,$ and unit weight of the soil under the footing is $125$ pounds per cubic foot. Using the Terzaghi bearing capacity formula and a factor of safety of $2\mathrm{.}5,$ determine:

a$)$ The width of the square footing when the bottom of the footing is $30$ in $.$ below the ground surface. b$)$ The volume of concrete in the footing if the bottom of the footing is at $5$ feet instead of $30$ in $.$