Take the midpoint e of AD and connect PE, then PE is the height of triangular pad. PE is perpendicular to AD.

Because the plane PAD is perpendicular to the plane ABCD, PE is perpendicular to the plane ABCD (two planes are perpendicular, and the straight line perpendicular to the intersection line in one plane must be perpendicular to the other plane).

Then draw the conclusion that PE is perpendicular to BD. ( 1)

In the triangle ADB, AD 2+BD 2 = 16+64 = 80.

AB^2= 16*5=80

Namely: AD 2+BD 2 = AB 2. Understanding angle: ADB=90 degrees.

That is, BD is perpendicular to AD. (2)

BD is perpendicular to the intersection line PE, AD. So BD is perpendicular to the plane PAD.

The plane MDB passes through the straight line BD, so the plane MBD is perpendicular to the plane PDA.

The plane perpendicular to the plane must be perpendicular to this plane.

(2) Find the volume: the height of the cone: PE=2* root number 3.

The bottom is trapezoidal, and its height is the height DF on the hypotenuse of the triangle ADB.

According to the proportional mean value theorem, BD 2 = AB * BF,

Namely: 64=(4 root numbers 5)*BF, BF= 16/ root numbers 5.

Then, from Pythagorean theorem, DF=8/ root number 5.

Upper base DC=2* radical number 5, lower base AB=4* radical number 5.

Base area: S=0.5*[2* root number 5+4* root number 5]*8/ root number 5.

=0.5*48=24.

Therefore, the volume v of the quadrangular cone = (1/3) * s * 2 * radical number 3=

= 16* root number 3.