Giải thích các bước giải:
a.Ta có :
$V_{ABC}=\dfrac{1}{3}.SA.S_{ABC}=\dfrac{1}{3}.SA.\dfrac{1}{2}.AB.BC=2a^3$
b.Ta có :
$\begin{split}\dfrac{V_{SMN}}{V_{SABC}}&=\dfrac{S_{SMN}}{S_{SBC}}\\&=\dfrac{SM.SN}{SB.SC}\\&=\dfrac{(SM.SB).(SN.SC)}{SB^2.SC^2}\\&=\dfrac{SA^2.SA^2}{SB^2.SC^2}\\&=\dfrac{SA^4}{(SA^2+AB^2)(SA^2+AC^2)}\\&=\dfrac{SA^4}{(SA^2+AB^2)(SA^2+AB^2+BC^2)}=\dfrac{9}{133}\end{split}$
$\rightarrow V_{SMN}=\dfrac{18a^3}{133}$