Another cut line on the development view

As shown in Fig. 1, there is cube ABCD-EFGH whose length of one side is 6 cm.

The points I and J are middle points of the sides AE and BF, respectively.

The points L and K are on the sides DH and CG, respectively and DL : LH = CK : KG.

This cube is cut by the plane which passes along four point I, J, K, and L, and it is divided into two solids.

Answer the following questions.

(1) When DL : LH = 1 : 2, find the volume of the solid including the vertex A.

(2) Draw the sides of the figure of the cut surface of (1) in the development view of Fig. 2.

(3) The ratio of the volume of a solid including the vertex A and a solid including the vertex E was 7 : 9.

Find the length of DL.

Answer