Slope volume calculation

If the same slope angle is to be recreated, I would virtually remove a cuboid 2.5m x 35m x 3.05m from the back (which needs to be disposed of) and shift the slope 2.5m backward. I could lend a few building blocks of my child for better visualization. So I don't think that the 755.9m³ is correct.

push the slope back by 2.5m.

This works wonderfully with building blocks, but in reality, a new slope must be dug out. So practically:

[*]Excavate old slope (volume of the triangular cross-section times 35 m length) [*]Excavate blocks (2.5 m offset times height times length) [*]Dig new slope (volume as in 1.)

I don't want to calculate again ... it must be correct :P

If the same slope angle is to be created again, then I would virtually remove a cuboid 2.5m x 35m x 3.05m at the back (which must be disposed of) and push the slope 2.5m backwards. I could lend a few building blocks of my child for better visualization.

So I don't think the 755.9m³ is correct.

Yes, it is correct. Initially, you have only created a hole where the slope has space - but it is still in its old place for you, so it must be removed and rebuilt on your remaining embankment.

One must be careful here about what is actually being moved - the total volume is, if you remove it in front and rebuild it at the back, ultimately even the same; which of course does not mean that the moved volume is zero.

Best regards Dirk Grafe

Well, he's not entirely wrong...

If you now assume that you really only dig up what is supposed to be removed, you would have a parallelogram with edge lengths of 2.5m and 5.5m. For the area, you need the height -> 3.05m. That would be the cuboid he takes out at the back.

That's the mentioned 262.5m³.

You don't have to dig up the entire embankment with 4.5m since it is only shifted back by 2.5m.

Parallelogram with side lengths of 2.5 m and 5.5 m

The base of the slope is 4.58 m long, plus the offset of 2.5 m. The parallelogram therefore has a base line of (4.58+2.5) m = 7.08 m.

A sketch would illustrate this ...

I think the OP means it differently because:

Top and bottom edge are set back by 2.50 m over a length of 35 m.

If he simply wants to shift the apex and base point back by 2.5 m, then the baseline is only 2.5 m as well...