The topographic map $($as shown above$)$ shows a site that is $280$ ft x $300$ ft overall, with a grid laid out as shown above. The grid size is $40$ ft x $50$ ft$.$ The current elevations are shown as dashed lines; the planned elevations are shown as solid lines. Calculate $(1)$ the volume of cut in cubic yards $(30$ points$)$ and $(2)$ the volume of fill in cubic yards $(30$ points$)$ required to bring this site to the new grades shown on the plan.