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