Đáp án:
$30)\quad B.\ \dfrac{a^3}{3}$
$31)\quad A.\ \dfrac V2$
Giải thích các bước giải:
$30)$
$\quad V_{S.ABCD}=\dfrac13S_{ABCD}.SA$
$\Rightarrow V_{S.ABCD}=\dfrac13\cdot a^2\cdot 2a$
$\Rightarrow V_{S.ABCD}=\dfrac{2a^3}{3}$
$\Rightarrow V_{S.ABC}=\dfrac12V_{S.ABCD}=\dfrac{a^3}{3}$
$31)$
Ta có:
$+)\quad AE = EB =\dfrac12AB\quad (gt)$
$\Rightarrow S_{AEC}=\dfrac12S_{ABC}=\dfrac14S_{ABCD}$
$+)\quad AF = FD =\dfrac12AD\quad (gt)$
$\Rightarrow S_{AFC}= \dfrac12S_{ACD}=\dfrac14S_{ABCD}$
$\Rightarrow S_{AECF}=\dfrac12S_{ABCD}$
$\Rightarrow \dfrac13S_{AECF}.d(S;(ABCD))= \dfrac12\cdot \dfrac13S_{ABCD}.d(S;(ABCD))$
$\Rightarrow V_{S.AECF}=\dfrac12V_{ABCD}$
$\Rightarrow V_{S.AECF}=\dfrac{V}{2}$
