The solution is AB=2√2.

△ ABC = AB 2+BC 2 with AC 2 is a right triangle with AC as the right.

Let m be the midpoint of AC and the radius of the ball be R.

Then the length of OC is the distance from o to plane ABC, and AC is the diameter of the circumscribed circle of △ABC.

get( 1/3)*( 1/2)* AB * BC * OM =( 1/3)*( 1/2)*(2√2)* 1 * OM =((。

OM=(√7)/2

R^2=(3/2)^2+((√7)/2)^2=4

So the surface area of the ball O = 4 π * 4 2 = 64 π.

I hope I can help you!