Can /sci solve this tusk. We have cube and 4 points in edjes. How to get volume of green area in pic?

bump

(l*w*h)/2

>Volume of green area
Trick question

Tusk too difficult. Four points have no common plane.

Just integrate 1 over the volume three times

you are right

min one point always in top min one always in bottom? wtf does this mean?

You can alway take the convex hull. Nobody said that the green shape has 6 sides rather than 7.

No one said the sectional cut is planar.

One point in top corner of cube another in bottom corner of cube, other always in edges but height might be different.

apply to 3d

Can we take it that the 3 lower points form a horizontal triangular plane, and that this connects to a second triangular plane made by the top corner and the 2 closer points?

Are the lower points at unspecified heights, or are they halfway up?

bump

I'm assuming [math]d\leq c\leq b\leq a\leq 1[/math]
I started working on a formula for volume in terms of a,b,c and d but it's really really fucking tedious and I can't be arsed. There are multiple formulae which depend on how many variables are equal to each other.

It's more straightforward to calculate the volumes of four tetrahedra and then subtract the overlaps (intersections).

That's got to be a harder way to do this... Actually there isn't.

0, you only shaded the faces of the cube :^)

7

good job, tnx

this is wrong though

Your question isn't clear enough since it is impossible to deduce your actual indication by the term "green area" led by your artistic implication of a cube. I assume that the 4 points are co-planar, and if I am correct, then the valoume should be (a2x) m3 where a is the length of a side of the cube and x is the height from base to the plane held by the 4 assumed co-planar points you "tried" to indicate.

X is actually the height of the plane from top. Now# the third point is not on a plane rather it is on a vertex keeping rest three points oon a plane, then I "think" that the volume would be half of ax2+a quarter of ax2. I wouldn't insist that I am correct and hence I welcome any counter propositions.

i'm coming back to retract my "add up the tetrahedra" approach

there's a region in the middle of the cube that's clearly inside the region of interest but not inside any of the tetrahedra
it should have been obvious when i was drawing the diagram, but i am an idiot

Is my approach even borderline "correct"?
*Pretentious use of words doesn't give me the feeling of being correct. It just feels to me dude :)*

/thread