Cube cut

The edge of the CC' guides the ABCDA'B'C'D'cube, a plane that divides the cube into two perpendicular four-sided and triangular prisms, whose volumes are 3:2. Determine which ratio the edge AB divides by this plane.

Correct answer:

r =  1:4

Step-by-step explanation:

V1:V2 = 3:2 V1 = S1 a V2 = S2 a S1:S2 = 3:2  S2 = 2ax S1 = a2  S2 = a2  2ax  (a2  2ax) / 2ax = 3:2 (2a2ax) / ax = 3:2 (2ax) / x = 3:2 2ax  = 1.5 x  2a  = 2.5 x  r = (ax)/x = (2.5x/2  x) /x  r=2.5/21=41=0.25=1:4

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