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Mathematics-Online problems:

Interactive Problem 69: Tetrahedron Intersected by a Plane

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
#./interaufg69_en.tex#The plane

$\displaystyle E: x+y=1 $

dissects the tetrahedron with vertices

$\displaystyle (x, y, z) = (0,0,0), (2,0,0), (0,3,0), (0,0,6) $

into two solid subfigures.


\includegraphics[width=.3\linewidth]{TdM_13_A3_bild}

Find the points of intersection $ A, B, C, D$ on the edges.
Compute the volumes of the tetrahedron and of the solid subfigure containing the origin $ O$.

Hint: The dashed triangle $ \triangle (C, P, Q)$ dissects one of the solid subfigures into a prism and a pyramid having a quadrilateral base.


Answer:

$ A = $ ( , , )    
$ B = $ ( , , )    
$ C = $ ( , , )    
$ D = $ ( , , )    
$ V_{\text{tetrahedron}} = $    
$ V_{\text{subfigure}} = $    
     

(The results should be correct to three decimal places.)


   

(From: Mathematics Contest 2013)

see also:

  automatically generated: 2/ 6/2018