Question

Answer 1

(1)

ta có: \(SA=\sqrt{SB^2-AB^2}=\sqrt{\left(5a^2\right)-\left(3a^2\right)}=4a\)

\(S=2a.3a=6a^2\)

V= \(\dfrac{1}{3}.S.SA=8a^3\)

Answer 2

(2) 

\(\left\{{}\begin{matrix}OA\perp OB\\OA\perp OC\end{matrix}\right.\Rightarrow OC\perp\left(OAB\right)\Rightarrow V=\dfrac{1}{3}.OC.S=\dfrac{OA.OB.OC}{6}=a^3\)

Answer 3

(3) 

\(\Delta SAB\perp A\)\(\Rightarrow SA=\sqrt{5a^2-a^2}=2a\)

\(v=\dfrac{1}{3}.SA.S=\dfrac{1}{3}.2a.\dfrac{1}{2}.a.\sqrt{3a^2-a^2}=\dfrac{a^3\sqrt{2}}{3}\)