Đáp án:
$V_{C'.MNK}= \dfrac{1}{12}V$
Giải thích các bước giải:
Ta có:
$\quad V_{C'.AB'C}= V - V_{A.A'B'C'} - V_{B'.ABC}$
$\Leftrightarrow V_{C'.AB'C}= V - \dfrac13V - \dfrac13V$
$\Leftrightarrow V_{C'.AB'C}=\dfrac13V$
Mặt khác:
$\quad S_{MNK}= S_{AB'C} - S_{MNC} - S_{AMK} - S_{KNB'}$
$\Leftrightarrow S_{MNK}= S_{AB'C} - \dfrac13S_{AB'C} - \dfrac14S_{AB'C} - \dfrac16S_{AB'C}$
$\Leftrightarrow S_{MNK} = \dfrac14S_{AB'C}$
Khi đó:
$\quad \dfrac13S_{MNK}.d(C';(AB'C))= \dfrac13\cdot \dfrac14S_{AB'C}.d(C';(AB'C))$
$\Leftrightarrow V_{C'.MNK}= \dfrac14V_{C'.AB'C}$
$\Leftrightarrow V_{C'.MNK}= \dfrac14\cdot \dfrac13V$
$\Leftrightarrow V_{C'.MNK}= \dfrac{1}{12}V$
