Lời giải

Chọn D

\(\Delta ABC:AC = a \Rightarrow AB = BC = \frac{{a\sqrt 2 }}{2}\)\( \Rightarrow {S_{ABC}} = \frac{1}{2}.\frac{{{a^2}}}{2} = \frac{{{a^2}}}{4}\).

\(\Delta SAC\) đều\( \Rightarrow SI = \frac{{a\sqrt 3 }}{2}\).

Thể tích khối chóp \(S.ABC\): \(V = \frac{1}{3}.SI.{S_{ABC}} = \frac{1}{3}.\frac{{a\sqrt 3 }}{2}.\frac{{{a^2}}}{4} = \frac{{{a^3}\sqrt 3 }}{{24}}\).