Does anyone know how to calculate the volume of this figure?

[s219]

None of the plane geometry formulas will work for this one. The slope of the 21' ends are equal but the slopes of the 55' sides are different. Because of this, you can't just use the average heights.

You know, I went back and derived it with variables in place of the numbers, and I get the same formula when I break it into simpler volumes as I get when using the average height. It holds true whether the top is a single plane or two planar triangles. If I was a mathematician I could probably explain why, but since I'm an engineer I can just say that's rather interesting .

 

[MossRoad]

You know, I went back and derived it with variables in place of the numbers, and I get the same formula when I break it into simpler volumes as I get when using the average height. It holds true whether the top is a single plane or two planar triangles. If I was a mathematician I could probably explain why, but since I'm an engineer I can just say that's rather interesting .

I seem to recall that formula for averaging the heights. Couldn't remember the formula, so can't remember when I heard it or from who, but I do recall it now....

This is why we need old folks to tell young folks simpler ways to figure stuff....

 

[Streetcar]

Make sure you have drainage behind the wall. Saturated soil is common failure method for walls

 

[jenkinsph]

I would guess this to be between 75 and 80 yards of fill depending on compaction. If you are building a barn on top of this I recommend you compact the fill in 4 to 6 inch layers. Drainage at the bottom of the retaining wall is very important too as others mention.