Solution: Let the center of the sphere be O, the center of the circumscribed circle of the triangle ABC be D and the radius be R. Because AB=3, AC=4 and AB is perpendicular to AC, the triangle ABC is a right triangle, so BC=5 is the diameter of the circumscribed circle of the triangle ABC, and OD is perpendicular to the circle D, because it is a straight triangular prism, AA 1= 12. Therefore, AD=5/2. So in the right triangle ODA, OA 2 = OD 2+AD 2, and the solution OA is the radius of the ball. To sum up, OA= 13/2.

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