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

[4570Man]

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. Here's a drawing of the dimensions if it helps.

 

[MossRoad]

I didn't know there was going to be a quiz....

 

[RNeumann]

It looks like 4 triangles that will need to be calculated separately. Then the rectangular areas are LxHxW. Remember to use all the same units of measure. It's easy to say 6 inches by 27 feet etc when it should be 0.5 feet by 27 feet. That will give you the cubic feet. Their are 27 cubic feet in a yard which is how concrete is ordered.

 

[RNeumann]

How to Calculate the Area of a Triangle (with Cheat Sheets)

 

[s219]

Did it two completely different ways and came up with 64.17 cubic yards both times.

For the simple approach -- take an average of all four heights, which works out to 1.5 feet. Then do 1.5 x 21 x 55 / 27.

 

[MossRoad]

Here's my guess.....

Cut it up into rectangles and triangles.

From top down, its basically a 22 x 55 X 3' rectangle sliced in half on a tilted diagonal sitting on top of a 22 x 55 x 1' rectangle, with one quarter missing.

So
22 x 55 x 3 = 3630 * .5 = 1815
plus
22 x 55 x 1 = 1210 x .75 = 907.5



EDIT: OOPs,
Forgot to cut my top rectangle in half... :mur:

1815 + 907.5 = 2722.5 / 27 cubic feet per yard = 100.83 yards.

 

[bcp]

Have them truck in fill until you can say "One more should do it."

Bruce

 

[4570Man]

Did it two completely different ways and came up with 64.17 cubic yards both times. For the simple approach -- take an average of all four heights, which works out to 1.5 feet. Then do 1.5 x 21 x 55 / 27.

That's how I did it before and came up with 67 yards.

 

[MossRoad]

Here's my guess.....

Cut it up into rectangles and triangles.

From top down, its basically a 22 x 55 X 3' rectangle sliced in half on a tilted diagonal sitting on top of a 22 x 55 x 1' rectangle, with one quarter missing.

So
22 x 55 x 3 = 3630 * .5 = 1815
plus
22 x 55 x 1 = 1210 x .75 = 907.5



EDIT: OOPs,
Forgot to cut my top rectangle in half... :mur:

1815 + 907.5 = 2722.5 / 27 cubic feet per yard = 100.83 yards.

Drew it up in sketchup and I guess its not half of the top rectangle, its a quarter....

So... one more time...

22 x 55 x 3 x .25 = 907.5
plus
22 x 55 x 1 x .75 = 907.5

907.5 + 907.5 / 27 = 67.222


Boy, pictures sure help! :laughing:

 

[4570Man]

Drew it up in sketchup and I guess its not half of the top rectangle, its a quarter.... So... one more time... 22 x 55 x 3 x .25 = 907.5 plus 22 x 55 x 1 x .75 = 907.5 907.5 + 907.5 / 27 = 67.222 Boy, pictures sure help! :laughing:

We got there different ways, but that's the same answer I got. Now how many yards of dirt are on a tri axel truck? Concrete isn't in the budget. We'll fill most of it with dirt and then gravel.