[Volume of a weird shape]

Using a famous BIM software (stating with a R) i found 56 m3 and by hand, I can't get closer than 61 m3 (by approximating the whole complex void as a simple rectangular pyramid)

[Volume of a weird shape]

Hello all!

I was in practicing BIM (building information modeling) at school when our teacher told us than crazy shapes aren't an issue anymore when it comes to determinating a volume since we can rely on computers. We now just have to draw it in 3D and softwares can give us the answer we need.

I was curious about how it was done before all that. Here's an example : From above, a rectangular shape. Corners at the same higher height are merging into a point at a lowest height. See attached picture. I tried to figure the volume by hand considering a whole rectangular parallelepiped from which I substracted parts of rectangular based pyramids. Well, turns out I can't manage do find the good answer.

Can anyone? I doubt it will bother you as much as it did bother me.

Cheers2553_001.pdf