



 
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  


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