cut/fill calculation tool to investigate if there is enough material to achieve a 30 degree slope

This is a cut/fill problem.

We have pits that have been dug in the ground, usually rectangular. They have a bund wall around them. They are being rehabilitated by pushing the bund back into the pit. Usually the bund is not enough to refill the pit. We need to achieve a maximum 30 degree slope between the original land surface outside the feature and the backfilled material pushed in from the bund. We need to know if we have enough material in the bunds to achieve this angle of slope.

We know the bund volume from topographic survey (interpolated the original land surface under the bund from elevation points outside the feature in the topographic data). From this interpolated surface we know the location and height from which the 30 degree slope will start and go down into the pit. Is there a tool in any GIS or CAD program that will take this line (as a polyline or polygon for example), take the angle (in this case 30 degrees) and output a new line or polygon showing where the topographic surface will be intersected, right the way around the pit? With this new line, a TIN could be created of the elevations along it at the bottom of the proposed slope and the elevations of the intersection at the top of the slope between the original land surface and the topographic surface. The topographic surface could then be subtracted from this new TIN to get the volume and see whether it is the same or less than the volume in the bund.

If there is a tool to automate this, it would make life much easier. Otherwise we could calculate a few points around the pit manually for a coarser estimate.