Using the average end area method, determine the required volume of the cuts and fills for a new road. The cuts and fills for each station are shown in Table $9\mathrm{.}1.$ Express your answer in cubic yards.

Table $9\mathrm{.}1$ Cut and Fill

$\backslash$table$[[$Station$,$Cut $($sf$),$Fill $($si$)],[10+00,0,0],[10+50,257,0],[11+00,175,50],[11+50,20,285],[12+00,0,233],[12+20,0,0]]$