There are four points A, B, C and D on the sphere with radius R. The quadrilateral ABCD is a square with side length R. Is there a point P on the sphere so that the volume of the quadrilateral P-ABCD is a cube of half R? If yes, please determine the location of the point; If it does not exist, please explain why.

Analysis: ∵ There are four points A, B, C and D on the sphere with radius R, and the quadrilateral ABCD is a square with side length R.

∴S(ABCD)=R^2

Suppose there is a point p on the sphere.

v(p-abcd)= 1/3r^2*h=r^3/2==>； h=3R/2

As shown in the figure: This figure is a cross-sectional view of the ball O along the diagonal AC of the bottom ABCD.

AC is the diagonal of the bottom ABCD, and the distance from the surface A'B'C'D' to the surface ABCD is 3R/2.

Then point P is on a circle with H as the center and HA' as the radius, which is perpendicular to the diameter FG of ball O.