Hi Steve,

This is a big hole you need to fill!

Here is my diagram, it is very much not to scale.

I am going to partition the volume into two parts as in the diagram below.

The top piece, shaded brown is a trapezoidal prism and its volume is

\[\frac12 (26 + 6) \times 20 \times 1.8 = 576 \mbox{ cubic metres.}\]

The piece shaded yellow is a wedge and its volume is

\[\frac16 \times 1.4 \times 20 \times (52 + 6) = 271 \mbox{ cubic metres.}\]

assume that the culvert pipe is parallel to the highway and is about halfway from the highway to the field. This it need to be about 16 m long and hence its volume is

\[\pi \frac{1.2}{2} \times 16 = 18 \mbox{ cubic metres.}\]

Thus the volume of stone you need is approximately

\[ 526 + 271 - 18 = 829 \mbox{ cubic metres.}\]

Harley