Hello, Tom!

1) An excavation for a farm dam is 30m long and 25m wide at ground level.

The sides slope down to a base that is 20m long and 10m wide.

The bottom of the dam is 3m below ground level.

Use the trapezodial rule with 5 sections to find an approximation for the volume. If I interpret the problem correctly, the hole looks this this: Code:

B *-------------------* C
* *
* *
* + * 20
* : *
* : *
A *-------------------* D
30 :
: 3
B'*---:-----------*C'
* : *
* + * 10
* *
A'*---------------*D'
20

There is a horizontal 30 × 20 rectangle $\displaystyle ABCD$ at the top.

There is a horizontal 20 × 10 rectangle $\displaystyle A'B'C'D'$ at the bottom.

The perpendicular distance between the rectangles is 3 m.

Draw $\displaystyle AA',\:BB',\:CC',\:DD'$.

We have a frustum of a rectangular pyramid.

Can you finish it now?