Cho Hình Chóp S. ABCD Có đáy ABCD Là Hình Thoi. Gọi D′ Là Trung ...

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Cho hình chóp S. ABCD có đáy ABCD là hình thoi. Gọi D′ là trung điểm SD , mặt phẳng chứa BD′ và song song với AC lần lượt cắt các cạnh SA , SC tại A′ và C′ . Biết thể tích khối chóp S. A′BC′D′ bằng 1 , tính thể tích V của khối chóp S. ABCD . A.V=92 . B.V=32 . C.V=6 . D.V=3 . Đáp án và lời giải Đáp án:D Lời giải:Lời giải Chọn D Gọi O là tâm hình bình hành đáy và I=SO∩BD′ . Mặt phẳng được nói đến đi qua I và song song AC nên cắt SAC theo giao tuyến là đường thẳng A′C′ qua I và song song AC . I là trọng tâm tam giác SBD nên SA′SA=SC′SC=SISO=23 . Ta có : VS. A′BD′VS. ABD=SA′SA. SD′SD=23. 12=13VS. BC′D′VS. BCD=SC′SC. SD′SD=23. 12=13⇔VS. A′BD′=16VVS. BC′D′=16V⇒VS. AB′C′D′=VS. A′BD′+VS. BC′D′=13V ⇒V=3VS. AB′C′D′=3 .

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