We also tested this question once. Let the height of ABCD be h, the side length a and AE=b, and it is easy to get H=√6/3a.

Because the shape of AEFG is exactly the same as that of ABCD, the height of AEFG also satisfies H' = √ 6/3b. BEFG height h=H-h'

Then v = √ 2/4a 3, and v' of BEFG = √ 2/4 (AB 2-B 3), and the derivative is taken to get the maximum value V' = √ 2/27a 3, that is, the ratio V'/V=4/27.