A rectangular foundation with LIB ratio of $2$ will support a column load, Q $=900$ kN$.$ The underlying soil$$is a dry sand with unit weight, $1$ d $=17\mathrm{.}5$ kN$/$m $3$ and an angle of internal friction of $35\backslash$deg A factor of safety of$3$ is required. Find the dimensions of the foundation if: $($a$)$ the foundation is placed at the ground surface; and$($b$)$ the foundation is placed $1$ m below the ground surface. For part $($b $),$ use a spreadsheet to solve the equation$$for B$.$ The equation should be of the form $0=$ f$($B$).$ Try B $=0\mathrm{.}4$ m to B $=1\mathrm{.}5$ musing increments$$of $0\mathrm{.}1$ m$.$ Turn in the spreadsheet as part of your solution.