Analysis: ∵ triangular pyramid S-ABC, base ABC is a regular triangle, AB= 1, SC is the diameter of the circumscribed sphere, and the center of the sphere is O, OC= 1.

∴ The cross section of the ball passing through SC and perpendicular to the bottom surface must be perpendicular to the bottom surface ABC, and pass through the midpoint D of the bottom edge AB, and the circumscribed circle of the triangle ABC of the revealing surface is at E.

CE is the diameter of the circumscribed circle of triangle ABC.

∴CE=2√3/3

∵SE⊥CE, ∴SE is the height at the base of a triangular pyramid, and se = √ (sc 2-ce 2) = √ (4-4/3) = 2 √ 6/3.

∴v(s-abc)= 1/3*se*s(⊿abc)= 1/3*2√6/3*√3/4=√2/6

Option a