Hình chóp S.ABCD đáy hình vuông, SAvuông góc với đáy, \(SA = a\sqrt 3 ,AC = a\sqrt 2 \). Khi đó thể tích khối chóp S.ABCD là
A. \(\frac{{{a^3}\sqrt 2 }}{2} \cdot \)
B. \(\frac{{{a^3}\sqrt 2 }}{3} \cdot \)
C. \(\frac{{{a^3}\sqrt 3 }}{2} \cdot \)
D. \(\frac{{{a^3}\sqrt 3 }}{3} \cdot \)
$\begin{array}{l}\left\{ \begin{array}{l}SA = a\sqrt 3 \\AB = AC.\cos \left( {{{45}^0}} \right) = a \Rightarrow {S_{ABCD}} = {a^2}\end{array} \right.{\rm{ }}\\ \Rightarrow {V_{S.ABCD}} = \frac{1}{3}SA.{S_{ABCD}} = \frac{{{a^3}\sqrt 3 }}{3}\end{array}$
A. \(\frac{{{a^3}\sqrt 2 }}{2} \cdot \)
B. \(\frac{{{a^3}\sqrt 2 }}{3} \cdot \)
C. \(\frac{{{a^3}\sqrt 3 }}{2} \cdot \)
D. \(\frac{{{a^3}\sqrt 3 }}{3} \cdot \)
$\begin{array}{l}\left\{ \begin{array}{l}SA = a\sqrt 3 \\AB = AC.\cos \left( {{{45}^0}} \right) = a \Rightarrow {S_{ABCD}} = {a^2}\end{array} \right.{\rm{ }}\\ \Rightarrow {V_{S.ABCD}} = \frac{1}{3}SA.{S_{ABCD}} = \frac{{{a^3}\sqrt 3 }}{3}\end{array}$