Problem $2$: $(25$ points$)$

Using the Prismoidal Formula, calculate the cut for a trench excavation which has the following geometry:

North Section:

$4$:$1$ side slopes on both sides

$4\text{'}$ depth

${10}^{\text{'}}$ trench bottom width

Middle Section:

$3$:$1$ side slopes on both sides

$3^{\text{'}}$ depth

${10}^{\text{'}}$ trench bottom width

South Section:

$2$:$1$ side slopes on both sides

$2\text{'}$ depth

${10}^{\text{'}}$ trench bottom width