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:

$$\begin{gathered} V_1:V_2=3:2 \\ {V}_1=S_{1}a \\ {V}_2=S_{2}a \\ {S}_1:S_2=3:2 \\ {S}_2=\frac{a_x}{2} \\ {S}_1=a^2-S_2=a^2-\frac{a_x}{2} \\ (a^2-\frac{a_x}{2})/\frac{a_x}{2}=3:2 \\ (2a^2-a_x)/a_x=3:2 \\ (2a-x)/x=3:2 \\ 2a-x=1.5x \\ 2a=2.5x \\ r=(a-x)/x=(2.5x/2-x)/x \\ r=2.5/2-1=\frac{1}{4}=0.25=1:4 \end{gathered}$$

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