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The problem of catching the ball in high school mathematics
EF is perpendicular to the common line of non-planar segment AB and CD, so the center of the ball is on EF.

Let the center of O be e, x and F(4-x).

Connect OA and OC, then OA=OC=R= spherical radius.

Pythagorean theorem:

AE? +EO? =OA? =OC? =OF? +CF?

4? +x? =(4-x)? +2?

16+x? = 16-8x+x? +4

8x=4,x= 1/2

r? =4? + 1/2? = 16+ 1/4=65/4

Sphere area =4πR? =4π×65/4=65π