Path or slope or something else???

I have an existing topo survey.  I also have a final restoration contour plan.  I am trying to work out the volume of mineral which cannot be extracted due to a pipeline running across the site.  I would be obliged if anyone could suggest the best route to determine this.  The pipeline 'corridor' is approx 40m and I don't need batters taking into account.

Any help appreciated!

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OK - use of an outline gives me what I needed - but how to calculate the volume of material within the strip??