Cho Khối Chóp S.ABCD Có đáy ABCD Là Hình Vuông Cạnh 2a ...

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Câu hỏi

Cho khối chóp S.ABCD có đáy ABCD là hình vuông cạnh 2a, , khoảng cách từ A đến mặt phẳng (SCD) bằng a. Thể tích của khối chóp đã cho bằng:        

A.

 

B.

 

C.

 

D.

 

Đáp án và lời giải Đáp án:D Lời giải:

Chọn D  Phương pháp: +) Gọi E, F lần lượt là trung điểm của AB và CD. +) Dựng  , chứng minh . +) Dựng . Chứng minh  +) Dựa vào định lí cosin và định lí Pytago, tính SH và tính . Vì  Kẻ  ta có  Ta có  Đặt  Ta có  Áp dụng định lí Cosin trong tam giác SEF ta có:   Xét tam giác vuông SHE có  Áp dụng định lí Pytago trong tam giác vuông SHE có:   Vậy  

 

Đáp án đúng là  D

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