∴O is the center of gravity of ⊿ABC

The projection h of point \a on the edge of PBC is the vertical center of △PBC.

∴PH⊥BC

Similarly, the projection of pa on PBC side is pH.

∴PA⊥BC

The projection of pa on the surface ABC is PO.

∴AO⊥BC.

CO⊥AB can be obtained in the same way.

O is ABC's favorite.

Because the center of gravity of ABC coincides with the vertical center, ABC is an equilateral triangle, that is, the triangular pyramid P-ABC is a regular triangular pyramid.

Let AB=x, then AO=x3,

∴PO=36―x23

∴v= 13×34x 2×36―x3 = 1 12 108 x4―X6，

Let f (x) = 108x4-x6, then f (x) = 6x3 (72-x2).

When x ∈ (0 0,62) and f(x) increase ∴; When x ∈ (62,63), f(x) decreases, so when x=62, f(x) reaches the maximum value of 36.