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

[fried1765]

This started out as trying to come up with a semi accurate amount of fill needed to fill a retaining wall. I've been unable to figure it out and it's turned into a personal mission. The shape has a rectangular base with one side being 4 feet high with the adjacent corner being 0 feet high. The other adjacent corners are 1 feet high. The rectangle is 22 feet by 55 feet. The only number I've came up with is 67 cubic yards. Here's a paper model I built.View attachment 496267 Here's a drawing of the dimensions if it helps. View attachment 496268

Take your model to the local high school (or Jr. college) math instructor/professor.
They will figure it out exactly for you!

 

[4570Man]

Take your model to the local high school (or Jr. college) math instructor/professor.
They will figure it out exactly for you!

That wound be my mom and she hadn't figured it out either. She said it's a calculus problem, and calculus was never her strong point.

 

[Egon]

Back when a Planimeter was used to calculate earth volumes.

It was a rather boring procedure.:drool:

 

[Tabasco Jack]

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.
A 3D model shows a volume of 62.715 CY. Add a factor for compaction based on the type of fill and you've got it.
But since we're talking dirt by the truckload, the difference between 62.7 and 67 cy isn't much.

Good luck with it.

 

[MossRoad]

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.
A 3D model shows a volume of 62.715 CY. Add a factor for compaction based on the type of fill and you've got it.
But since we're talking dirt by the truckload, the difference between 62.7 and 67 cy isn't much.

Good luck with it.

The sides aren't 21, they are 22.

 

[Tabasco Jack]

The sides aren't 21, they are 22.

That dyslexia will get you every time.
67.07 CY

Here's the topo based on a 1' contour if you like.

 

[jel1988]

Now that the actual yardage has been calculated no one has considered a compaction factor ie. fluff. Depending on the material this could range from 0 using clean 3/4 crushed stone to 40% using some clay fills. For A gravel, usually what I use for the drainage layer behind the wall 10 to 15% should be added to allow for compaction.

 

[s219]

So the OP has 22' listed in the post but 21' on the sketch -- which is it??

I get 64.17 yards if it's 21' or 67.22 yards if it's 22'.

 

[MossRoad]

AHHHH!!!!!


:laughing:

 

[4570Man]

It's actually going to be 24 feet because we may build a pole barn over it in the future and 24' trusses are cheaper. The original sketch ( not pictured ) was 21x52 and I increased it to 22x55 for increased margin of error.