(1) First make a straight line OE perpendicular to AB through O to intersect AB at E and connect PE, then make a straight line OG perpendicular to PE through O to intersect PE at G; and make a straight line OF perpendicular to AD through O to intersect AD at F.

Then it can be found that:

Angle PFO is equal to the dihedral angle P-AD-B is 45; OG is perpendicular to pmPAB; angle OAG is equal to the angle formed by OA and angle formed by pmPAB

Because triangle PAD is isosceles, it is not difficult to find PF=2 root 2

Triangle FPO is an isosceles RT triangle, so PO=OF=2=FA,

And OF is perpendicular to AF, AF is perpendicular to AE, AE is perpendicular to OE, OF//AE, OF=AF, so quadrilateral AEOF is square,

so AO=2 root 2, AE=2,

so OG=root 2,

so sin angle OAG=1/2,

so the angle made by OA and pmPAB is 30.

(2) From (1) it is not difficult to derive that PE=2 root 2,

set AB= x, PB=y,

then we have (root 3)/3=(12+x^2-y^2)/4(root 3)x,

and x+y=8,

so AB=x=(find out for yourself.)

So the volume of the cone sought is

AD x AB x 1/2 x PO x 1/3 = (find it yourself 。。。。)