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I would like to know the volume of the intersection of a cone and a cuboid :

len=150;
wid=70;
dep=600;

phi=30;

vol1[h_] := Cone[{{len/2, wid/2, 0}, {len/2, wid/2, -h}}, h*Tan[phi Degree]];

vol2 = 
  Parallelepiped[{0, 0, 0}, {{len, 0, 0}, {0, wid, 0},
    {0, 0, -dep}}];

RegionIntersection[vol2, vol1[200]];

Volume[%]

But this doesn't work..

Could you help me ?

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  • $\begingroup$ Might help: mathematica.stackexchange.com/questions/51980/…. $\endgroup$ – anderstood Nov 26 '15 at 16:01
  • $\begingroup$ You should give values to longueur,largeur,profondeur and phi. $\endgroup$ – anderstood Nov 26 '15 at 16:02
  • $\begingroup$ I've forgotten this part of the code, it's now added $\endgroup$ – Alexis Rosuel Nov 26 '15 at 16:05
  • $\begingroup$ Works for me in 10.3, result 2100000-(125 (420 Sqrt[274]+686 ArcSinh[15/7]-3375 Log[-7+Sqrt[274]]+3375 Log[7+Sqrt[274]]))/Sqrt[3] $\endgroup$ – Simon Woods Nov 26 '15 at 16:09
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    $\begingroup$ If you are okay with an inexact result you could use machine precision values for the inputs (e.g. 150.0 instead of 150) which will be much faster $\endgroup$ – Simon Woods Nov 26 '15 at 16:17