Calculating the volume of cutted cone by a plane

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enter image description hereenter image description hereI need to calculate the volume bounded by the plane: $x+y+z=5$ and by the cone $z^2 = x^2 + y^2$, som my V that i'm $dv$-ing on it is cutted cone in non simetric way (i can find the equation of the intersection, but it dont give me anything).

As i see it, i need to find D and do the double integral on the substraction between my plane and the cone, am i right ?

And in that case, if i understand correctly, i need to find my D, but because it is a cone, i need only to find my R and i dont understnd which is it and how to find him (do i take the max or min - it is a cutted cone, so its upper part is by "diagonal" if we look at it in 3D). I hope i explain myself good enough.

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This doesn't really constitute an answer. I can delete it if it is not appropriate. I just want to show the following picture:

enter image description here

You can see this really doesn't enclose any volume to calculate.