Cube cut

In the ABCDA'B'C'D'cube, it is guided by the edge of the CC' a plane witch dividing the cube into two perpendicular four-sided and triangular prisms, whose volumes are 3:2. Determine in which ratio the edge AB is divided by this plane.

Correct result:

r =  1:4

Solution:

V1:V2=3:2 V1=S1 a V2=S2 a S1:S2=3:2  S2=ax2 S1=a2S2=a2ax2  (a2ax2)/ax2=3:2 (2a2ax)/ax=3:2 (2ax)/x=3:2 2ax=1.5 x  2a=2.5 x  r=(ax)/x=(2.5x/2x)/x  r=2.5/21=14=0.25=1:4



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