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Bài 8.31 trang 83 SGK Toán 11 tập 2 - Cùng khám phá

Cho hình hộp ABCD.A’B’C’D’ có ABCD là hình chữ nhật, AB = 3a và AD = 4a.
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Đề bài

Cho hình hộp ABCD.A’B’C’D’ có ABCD là hình chữ nhật, AB = 3a và AD = 4a. Hình chiếu vuông góc của A’ trên mặt phẳng (ABCD) là trung điểm của AD và AA’ = 4a. Tính thể tích khối hộp này.

Phương pháp giải - Xem chi tiết

Công thức tính thể tích hình hộp: V = S.h với S là diện tích đáy, h là chiều cao.

Lời giải chi tiết

Gọi E là trung điểm của AD nên AE = 2a\(A'E = \sqrt {AA{'^2} - A{E^2}}  = \sqrt {{{\left( {4a} \right)}^2} - {{\left( {2a} \right)}^2}}  = 2\sqrt 3 a\)\(V = S.h = AB.AD.A'E = 3a.4a.2\sqrt 3 a = 24\sqrt 3 {a^3}\)

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